First Direct customers have faced days of struggling to access their online banking, after the firm overhauled its log-in procedures.
First Direct says its online service is getting back to normal.
All 700,000 online customers have been told they must set a new user name and personal questions as the bank tries to make its internet service more secure.
This began on Friday - leading to a surge of people trying to access the bank's website over the weekend.
First Direct said the situation was gradually getting back to normal.
But on Tuesday afternoon, many users found the website was still out of action.
The volume of people trying to log on and change their details had caused a spike in users which the site had struggled to cope with, spokeswoman Amanda Brown said.
Tuesday's surge in traffic to the site may have been caused by "a lag of people frustrated from over the weekend" making further attempts to access internet banking, she added. Users have also had long waits getting through to the bank's telephone call centre - because of customers ringing up complaining that they could not log on.
Some who had managed to set up their new details had later forgotten them and locked themselves out of the system, adding to the pressure on call centre staff, Ms Brown said.
Customers experiencing problems should wait for a little while and try again later, she said.
"The levels of demand are coming down and we are now operating at more normal level."
BBC News Interactive readers said they had been left exasperated by the problems.
One user, Kevin Davis, said: "This must be costing millions to customers who need to make payments and get online.
"One presumes it will hit First Direct hard because I, for one, will now consider moving, if this demonstrates their level of care and service."
Users of Apple Mac computers have also been upset that the new online banking system does not support Safari - the default internet browser on Apple computers.
First Direct is already in the spotlight after it angered consumer groups by bringing in a £10 monthly fee for customers who do not pay in or keep a balance of at least £1,500 a month.
The fee will be waived if customers open a savings account or buy products such as home insurance or loans.
The bank said the move was aimed at dormant or rarely-used accounts.
Yes, this has been a delay in obtaining access into the online banking system, but lets be honest, First Direct have sent out details to its customers advising them of the fact that this change would be happening, in addition, it is trying to ensure that the customers details are further protected - personally, I think that the approach should be commended.
Richard Challis, Sale, England
I've not had any problems at all. I changed my security details on Thursday last week, and I've been able to log on without problems each day since. Just checked again tonight - and succeeded at first attempt . . . . I'm also pleased to report that there are no problems using Opera as a browser. No complaints from me!
Simon Longley, Derby UK
I am amazed anyone still banks with FD. I ditched them last year over their ridiculous charging structure. Vote with your feet there is plenty of choice around.
Ian Cooper, Dorset, England
Had absolutely no problem with the security upgrade. Haven't had to connect again since so maybe I missed the hassle. But *everyone* should agree with the upgrade ... definitely makes me feel more secure. Also, a tip for Mac users. Really (no really) easy to install Firefox on the Mac. Excellent browser ... much better than Safari. P.S. don't blame FD for not supporting Safari ... blame Apple for producing a sub-standard browser.
Paul, London, UK
I understand the need for better security, however, the systems really ought to be more user friendly. I contacted FD but got an indignant email saying "sorry that you had to waste your time" and that I should "use mis-spelled or reversed words" in my answers - because that's really easy to remember!
Colin M, Seattle, USA