Lawyers for more than a dozen British residents with ties to Iran accuse RBS and Natwest of racism.
Royal Bank of Scotland boss Ross McEwan admitted that it had failed to invest properly in systems for decades.
NatWest and Nationwide say they have solved their earlier computer glitches that had affected customers' accounts.
Mobile customers of Barclays, NatWest and RBS are enduring a difficult final day of the month - payday for many Britons - after being locked out of their banking apps.
All three banks announced problems with their apps on their Twitter accounts, saying:
We’re aware that there are issues with accessing our Barclays Mobile Banking app; this is being looked into on an urgent basis. 1/2
We’re aware of some issues on our Mobile Banking service and are working hard to fix them. Sorry and thanks for your patience.
If you’re having difficulty with our mobile app, online banking, telephone banking and ATMs are all working normally.
The trio urged their customers to use online banking, telephone banking, ATMs or visit a local branch to deal with their money issue or pay a bill.
Royal Bank of Scotland will offer three-month mortgage repayment breaks to customers with flooded homes.
Full details, including how to apply for the scheme will be released tomorrow by the group, which includes NatWest.
It said it would also send specialist business support teams to affected areas in coming weeks to help small businesses with short-term financial problems as they carry out repairs and suffer lost trading income.
NatWest have been struck by another technical blunder which has left some customers short-changed on their monthly interest payments.
Some NatWest and Royal Bank of Scotland (RBS) customers checking their E-Isa balances found they had been updated with just a few pence worth of interest in some cases.
A spokeswoman for RBS/NatWest described the error as an isolated incident and said customers' balances are being updated with the correct amounts as a matter of urgency.
Those who have found a mistake do not need to contact the bank as it will be automatically fixed.
While this latest failure is not IT-related, the bank has been beset by a string of technological errors in recent months.
Just days after that incident, the bank's websites were the victim of a cyber attack that left some customers unable to access their accounts.
NatWest has apologised to customers after its online service were disrupted by a 'denial-of-service' cyber attack. In a statement, a spokesperson said:
Due to a surge in internet traffic deliberately directed at the NatWest website, some of our customers experienced difficulties accessing our customer web sites this evening.
This deliberate surge of traffic is commonly known as a distributed denial of service (DDoS) attack. We have taken the appropriate action to restore the affected web sites.
At no time was there any risk to customers. We apologise for the inconvenience cause.
As reports emerge of online banking issues with NatWest, ITV News has asked whether you were affected tonight.
– Amy Walker
Yes I was affected by it. Wish I never banked with this bank worst ever.
– Colin Crotty
I just used mine no problems.
– Kirsty Butler
Nope I have logged onto my NatWest account twice today and transferred money not a problem.
Join in the conversation on the ITV News Facebook page
NatWest has said that its online banking system is now working after customers reported problems transferring money and using the site.
Sorry if you couldn't use Online Banking earlier. It's now working again, thanks for your patience.
NatWest customers are continuing to report issues with transferring money as the online banking system apparently faced a glitch tonight.
@suswatibasu I was not able to access my NatWest account to transfer money.
Asked whether Mr Curry was receiving any error messages, he responded:
@suswatibasu I got the message 'service is temporarily unavailable', while I was standing at the till at Tesco. Embarrassing.
A NatWest customer has told ITV News that there have been problems accessing the online banking site. Ben Jeffrey added that payments online are "not being authorised".
@suswatibasu Hi, unable to access the online banking website but the apps ok. Tried purchasing something online which rejected for no reason
@suswatibasu The only error message at all is that the website server is not responding. Explains why payments won't process
@suswatibasu after double checking, the website is working but still cannot get authorisation for payments online. Causing suspended account
NatWest customers are reporting problems with its online banking service, just weeks after another IT systems breakdown.
Natwest Online Banking still down? Doing my head in.
Natwest has gone down again... Bravo