At talks between the Civil Aviation Authority (CAA), airlines, regulators, and aircraft and engine manufacturers a new "time limited zone" was set up.
From midday on Tuesday this will allow planes to fly for a limited period when volcanic ash is present in the air at higher ash densities than currently permitted.
The CAA said airlines had to present it with safety information - including the agreement of their aircraft and engine manufacturers - to be allowed to fly in the new zone.
CAA chief executive Andrew Haines said unprecedented situations required new measures and the challenge posed by the volcano could not be "underestimated".
He said: "The world's top scientists tell us that we must not simply assume the effects of this volcano will be the same as others elsewhere.
"Its proximity to the UK, the length of time it is continuously erupting and the weather patterns are all exceptional features."
Jim French, chief executive of budget airline Flybe - the only airline so far to satisfy the CAA's conditions - said he welcomed the move.
He said the airline had been forced to cancel 381 flights during the past 48 hours but if the new criteria had already been in place, it would have only affected 21 flights.
Transport Secretary Philip Hammond said the CAA, aircraft and engine manufacturers and airlines had been working "extremely hard" to "get people flying".
Weather forecasters said the ash cloud from Iceland was now being blown away.
However, there may be some restrictions to helicopter operations in the North Sea, where a no-fly zone is still in force.
Across the country:
, flights were able to operate from all three of Northern Ireland's airport from 1300 BST, but delays and cancellations were still possible.
flights were cancelled for the rest of the day in Orkney and the Shetland Islands while Scotland's other airports reopened.
airports are open. However Cardiff airport is warning that some disruptions and cancellations remain in place following earlier restrictions.
Airport operators are advising passengers to check for delays to their flights with airlines, who are working to clear the backlog of delayed passengers.
By the time restrictions were lifted on Monday, flights were cancelled or delayed by up to six hours at the UK's major airports.
NATS Director Ian Hall: "We are looking forward to a change in the wind direction."
Thousands of passengers were left to rebook their flights or to wait in airports for new departure times.
Network Rail pledged to do everything possible to help stranded and delayed travellers make journeys by train.
Virgin Trains said 7,000 extra seats had been made available on Monday, mainly on routes between Birmingham and Glasgow and Edinburgh, and between London Euston and Glasgow.
Eurostar laid on six extra trains through the Channel Tunnel on Monday, amounting to about 5,500 additional seats.
In the Netherlands, Amsterdam's Schiphol and Rotterdam airports reopened from 1300 local time (1200 BST) after being closed for seven hours.
Since the Eyjafjallajokull volcano erupted last month, throwing huge amounts of ash into the air, thousands of flights have been delayed or cancelled across Europe due to fears that ash could turn into molten glass within a hot jet engine, crippling the aircraft.
Ash cloud forecast
The latest UK disruption saw airspace over Northern Ireland close first on Saturday, before the cloud moved south and grounded flights in many parts of the UK on Sunday.
Among the affected travellers who contacted the BBC News website was Matt Pope, from Guildford, who e-mailed to say it was the third time the ash had disrupted his travel plans. On the first occasion he was stuck in North Carolina for six days.
He wrote: "Last weekend the Easyjet flight from Prague to Gatwick was cancelled due to aircraft positioning problems after ash in central Europe.
"This was after we ran the marathon and I missed my flight to Singapore the next day causing expensive rescheduling.
"Now I am sat at Heathrow awaiting for a flight to NY. Will this ever end?"
Flight restrictions depend on how dense the ash cloud is.
The Civil Aviation Authority (CAA) had already raised the density threshold level that forces a flight ban, following six days of airport closures last month.
But after the latest airport closures over the weekend, airlines criticised the amended regulations.
British Airways chief executive Mr Walsh said: "I am very concerned that we have decisions on opening and closing of airports based on a theoretical model.
"There was no evidence of ash in the skies over London today, yet Heathrow was closed."
He said that airlines flew safely in other parts of the world where there was volcanic activity.
On Sunday, Virgin Atlantic president Sir Richard Branson called the closure of Manchester airport "beyond a joke".
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