Promoters SJM doubled the number of gigs on the tour in the UK and Ireland to 26, amid massive demand as box offices opened at 0900 GMT.
The boy band are to go on the road 10 years after they split up - but without former member Robbie Williams.
Some fans said they had trouble getting through to venues and booking agencies, who also began to sell tickets for gigs by The Rolling Stones and The Strokes.
Ticket brokers said their booking systems had been able to cope with the increased demand on Friday.
"People may have to wait a bit longer but our system is operating normally," said a spokesperson for Ticketmaster.
"Take That tickets are moving incredibly quickly," said a spokesperson for Seetickets. "We've been very busy but people are getting through."
Fans attempting to buy tickets for Wembley Arena experienced difficulties accessing the venue's website earlier in the day because of the massive demand.
Wembley said the site was working and advised that people would be able to purchase tickets if they kept trying.
Visitors to websites at other venues also said they experienced similar problems.
Promoters said Take That had sold more than 250,000 tickets, including 80,000 tickets in their hometown of Manchester and six nights at Wembley Arena in London.
Extra dates on their tour in April and May next year were added in London, Newcastle, Birmingham, Manchester and Dublin.
Take That's Gary Barlow said the group was "amazed" by the response to the tour.
"We always knew our fans were great, as they used to follow us around, but the response from them today has been overwhelming and we are so grateful for their loyalty and support."
The Rolling Stones have added a second date to the UK leg of their A Bigger Bang tour at Wembley stadium on 22 August. Their first concert at the venue on 20 August sold out in less than an hour, a spokesman said.
Have you had difficulties purchasing Take That tickets? A selection of your comments will appear here. This debate is now closed. Thank you for your comments
I had spent over two hours this morning trying to access a number of sites (Ticketmaster, Ticketline, Aloud.com and the NEC group) to buy tickets for my wife, but to no avail. All sites were swamped, unavailable or out of service and the phone lines were just as bad - permanently engaged. Eventually I had to drive to the NEC Box Office and buy them in person.
Matthew Evans, Birmingham, UK
I just managed to get tickets having been on line since bang on nine this morning. I got tickets directly from the Wembley website for 25 May but the seat at right at the back of the arena - still better than nothing!!!
I have tried since 9am this morning for tickets from Hallam FM Arena and have had no luck whatsoever. I have tried websites Seetickets, Ticketmaster etc... and have had no luck at all. I am really disappointed. Please Take That add more dates.
Dawn Outram, Worksop, Notts
I spent over two and a half hours trying to get tickets on four different websites and every time I got close the websites shut down. Two of the websites didn't even say when tickets were sold out! What a waste of time!!!
Sarah O'Hanlon, Nantwich
I tried from 9am. All I wanted was five tickets for my family to go. I was trying the websites and I was just going round in circles, the same as the phones. I finally managed to get three tickets at 2:30 this afternoon. It annoys me that people buy tickets and go on to sell them on eBay. Those tickets could have gone to someone who really wanted them and couldn't get them.
My daughter and myself have been trying the internet and phone all day separately and neither of us have got through, are all dates on sale?
Janet Hardman, Manchester
I had no problems getting my tickets this morning, but I did note that Ticketmaster's online service opened a few minutes earlier than expected, meaning that I was just lucky... I think Matthew Evans who bought tickets for his wife is my hero!
Georgia Burns, Newcastle, UK
Two hours wasted, flitting between all the different websites and phone numbers with no luck what so ever! Only to hear that I can only get them from the sharks that are now selling them on eBay for 10 times the ticket value. What can I do to get tickets the legitimate way???
Julie Gray, Fareham, Hampshire
I couldn't get away from work to get tickets for either the Glasgow or Newcastle gig. Ticketmaster etc were my only option. I am left very disappointed and what makes me angry is that people who didn't actually want the tickets are selling them on eBay for £500 a shot which wasn't very fair on the true fans.
Emma , Bathgate, Scotland
I tried from 9am this morning when the tickets went on sale and it took me over an hour and a half to get them with the use of many windows open and this was only when the second extra Manchester date was added. It'll be well worth it though!
The websites were a nightmare, none of them working and phone lines constantly jammed. They need to do something to improve the situation.
Emma Castle, Edinburgh
I spent over three and a half hours trying to buy tickets this morning from all the online sites and on the phone as well. Luckily I finally managed to buy the tickets online from Seetickets. I was rather frustrated at the time but I feel very lucky now!
Claire Lokie, Harrogate, UK
I started trying to get tickets from the internet from 9am. I had huge problems trying to even access the web pages and when I finally could all the tickets had sold out. I refreshed the page one last time to see a new date had been added and got them there and then. Less than five minutes later that new date had sold out as well. I'm so happy though!
I spent from 8:50 to past midday trying to get tickets. The phone lines were jammed and all internet sites were too busy to handle the demand. But with luck at just after midday I finally got the tickets (not the best in the world). I am pleased but do feel sorry for the true fans whom where not able to be as lucky. I just hope people don't start selling them at high prices.
James Moore, Aldershot, Hampshire
I had no luck trying to get tickets either on the SECC website or Ticketmaster or on the telephone. As usual people in Scotland find it harder to get tickets due to the fact that there are only two dates in Glasgow for the whole of Scotland. There should be more than two dates or they should be playing more places in Scotland than just Glasgow.
Alison Sherriffs, Aberdeen
I logged on at 9am and had my tickets from Ticketmaster by 9.10am.
I was trying from 8.45 this morning with no such luck. All the internet sites and phone lines where jammed. I am so frustrated.. it wasn't this difficult to get tickets first time around.
Emma, Manchester, England
There are five people in our office, and we all managed to get tickets to the venues we wanted via Ticketmaster. Yes it was busy, but sticking with the same website obviously work for us.
Took me almost two hours, but with some perseverance on the Ticketmaster website I finally got two tickets so I could take my fiance. Had to wait for the third lot of extra shows to be released, but it was a huge relief when they were.
Rob, Manchester, England
I tried from 9.00 this morning to get tickets from the Ticketmaster website, and also aloud.com. Both websites said no seats available but I eventually got through on the phones at 12.30 and got two seats at Newcastle
Such was my determination to get tickets that I took the day off work! Seems like I hadn't underestimated the scramble for tickets as I couldn't access one website, and that was trying from before 9am. Decided to give the websites a miss and concentrate on the phone lines. I finally got through to the MEN, only to find that both dates were completely sold out. Luckily it seems as though I got through as they released the third date and was able to get my four tickets.
Lizzie G, Poole, Dorset
I was online before 9am and searched for the best available tickets for the Wembley gig on 8 May. At 9.01am I got a page telling me that the best available ticket was in the upper side tier near the corner. I tried throughout the day and as more and more dates were added I was never able to get anything near the front. The ticket agencies need to be much more transparent about what tickets they actually have on sale.
I have been trying since 9am this morning for the Newcastle dates. I have had no luck at all. The websites kept crashing and the phone lines were constantly engaged. Very disappointed that I haven't been fortunate enough, especially as the tickets were on eBay by 10am this morning for ridiculous amounts of money. Please add more dates to Newcastle so those of us who haven't been lucky enough to get tickets so far can go!
I logged on at 8.45, unable to access the Sheffield Hallam FM Arena website. The Sheffield Arena box office hotline was jammed all morning. I tried Ticketmaster etc but all jammed. Very disappointed. I hope its not another 10 years before they tour again.
I managed to get tickets for Birmingham via the ticketline phone number and have got a ticket and bus for £60 which I feel is well worth it. Think yourself lucky in England, Scotland, N Ireland, Ireland. They didn't put on any dates in Cardiff!
I was on the phone and the websites from nine this morning. On the Wembley site I booked tickets and gave all my details but the site crashed before the order had gone through. This happened on many occasions and was very frustrating as each time I had to start again, and each time I started again more of the dates had sold out. I managed to get some from Ticketmaster when they had announced a new date.
Absolutely gutted. I have been phoning and going online since 10 this morning - constantly engaged and the web continually failing. I refuse to pay hundreds of pounds. Oh well maybe next year!!
Joanna Brown, Birmingham
I queued at the NEC box office from 5.15am. By 9 I was wet and tired, but I got fourth row tickets. I have tried websites and phone lines before, and decided the only way to make sure I had tickets was to buy them in person.
Finally got tickets to the last date in Wembley after the gig was added. The websites were either jammed or out of date. I got through the automated booking only to find that there were no tickets available and they had not been updated with the extra dates. It was an utter shambles and didn't represent the professionalism of the boys.
I went on Ticketmaster at 9am and was lucky enough to come across two tickets by 9.45am. I feel sorry for anyone who hasn't managed to get any, but I'm certainly not complaining. My mate actually tried to get me to put them on eBay, she said I could make my money back 10 times over. But this isn't about the profit, I've been waiting for Take That to reform for nearly 10 years. It's a dream come true, and I wouldn't trade them in for the world.
Natasha Bowie, Wellingborough, Northamptonshire
I must have been very lucky. I logged into Ticketmaster just before 8.55am, kept refreshing until 9am and got through without any problems. I can't believe that I actually got Row 9 seats for Take That in Belfast
Kathy, Northern Ireland
I was lucky enough to fluke two tickets for the Sheffield gig from Seetickets.com, but that was after trying for Newcastle tickets for three hours. So although I have to travel and stay in Sheffield, I suppose I'm one of the lucky ones!
Tried for three hours from nine to get tickets from NEC on website but kept crashing never got anywhere near to booking. Phone line constantly engaged. Ticketmaster not much better eventually luckily got some elsewhere for Wembley. Surely there must be something the venues can do to stop the sale of tickets on places like eBay so only those who genuinely want to go can get tickets.
Sarah Ventrella, Cheltenham, Glos
I spent four hours today trying to get tickets for the NEC. I reached the payment screens of the NEC website twice but then it froze. I eventually got a message telling me that my order had been processed but there was also an error message on the screen. I had to call the NEC technical team to find out what was going on. They confirmed that my order had been processed and I had four tickets.
Rob Clarke, West Midlands
I tried on Ticketmaster as soon as I got into work to get some tickets for my sister and a couple of her friends. Sadly, no luck, simply no chance if you weren't online before 9.10. My sister resigned to defeat, I persevered, and by 11am, the new dates showed up. Three tickets right near the front! My sister overjoyed, she now simply has to wait six months.
I was lucky enough to book four consecutive nights in a row. Each night I get closer and closer to the boys! Lucky Me! (with a very understanding husband)
Kerry Brant, Bournemouth, Dorset
Ticketmaster worked very well!! I got tickets for Dublin and London!
My sister has been trying Ticketmaster all day - I went on the Wembley site at 3.30pm and got five tickets straight away. Just tried to revisit it for a friend and now all gone.
I tried to call Wembley at 8.45am and it was engaged even then! I think the tickets went on sale at about 8.55am because all the best things had gone by 9am. I eventually got tickets for the Wembley 26 May date - at gone one in the afternoon! I couldn't believe the rate they were selling out. Unbelievable!
Nicola, Eastbourne, East Sussex
I tried for two-and-a-half hours, using different windows and websites! Eventually getting through to Ticketmaster. So relieved I got tickets! It was a nightmare. I think its disgusting that so many people are just buying them to sell on eBay at ridiculous prices....this needs to stop!