HSBC says it "successfully defended" an attack on its online banking system but services are disrupted on a key day for many people's personal finances.
The bank is apologising to customers trying to login to its online banking which, for many, is unavailable.
It said it was working with the authorities to "pursue the criminals responsible".
The final Friday in January is payday for lots of people and is also two days ahead of a key deadline for paying tax.
Sunday is the last day for filing self-assessment tax forms online and is when millions of the self-employed and others settle their tax bill with HM Revenue and Customs (HMRC).
Late payments face a 3% interest charge from HMRC, but the tax authority said there were many different payment options that could be used by the end of 31 January.
"Where taxpayers need information from their HSBC account, and they are currently unable to access this they can include an estimate in their return in order to file by 31 January. They have 12 months from the date they file to amend this with the correct information," a spokesman for HMRC said.
HSBC said that no customer details had been compromised by the attack and that it was "working closely with law enforcement authorities to pursue the criminals responsible".
"HSBC internet banking came under a denial of service attack this morning, which affected personal banking websites in the UK," said a spokesman for the bank.
"HSBC has successfully defended against the attack, and customer transactions were not affected. We are working hard to restore services, and normal service is now being resumed. We apologise for any inconvenience this incident may have caused."
The service had not resumed for most customers by mid-afternoon and the bank confirmed it was still working on a complete fix.
Victims of such attacks in the last month include the Irish National Lottery and the BBC. Banks are said to face these attacks on a daily basis, according to banking sources, and some of the High Street names have seen their websites affected.
It is not the first time this month that HSBC customers have faced a suspension of the service. HSBC customers faced two days of problems with online banking at the start of January.
The upheaval on that occasion was blamed on "a complex technical issue within our systems" by the bank.
More significant payment failures last summer at HSBC were this week revealed to have been the result of a backlog caused by a mega-payment sent to BACS - the system that processes electronic payments in the UK - exceeding the £1bn limit placed on the system.
Many banks suffer technical glitches with online banking, but the speed with which these issues are resolved is often the key source of concern for customers.