"HSBC UK Internet banking was attacked this morning. We successfully defended our systems," HSBC UK tweeted.
The bank has 17 million personal and business customers in Britain but did not say how many were affected.
John Hackett, HSBC's UK chief operating officer, added: "HSBC's Internet and mobile services have partially recovered, and we continue to work to restore a full service."
The disruption came on payday for many Britons and just days ahead a January 31 deadline for self-employed individuals to pay tax.
HSBC said it would waive fees incurred by customers as a result of the incident.
A spokesman identified it as a "denial of service attack", which slows down or disables a network by flooding it with communication requests.
Users attempting to access the bank online were met with a message saying: "Sorry, there appears to be a system problem. Please try again later."
Many customers took to Twitter to vent their frustration at the problems in accessing their accounts.
"I was planning to do something this weekend but I have zero clue how much money I have to play with due to @HSBC_UK_Help online banking down," wrote one, Jeston Westmoreland.
HSBC, Europe's biggest bank, suffered a series of online banking glitches earlier this month but said it was due to a technical problem not a cyber-attack.
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