We will work with our customers and the other banks including providing compensation where appropriate.
"Customers who do not receive the delayed payment by Saturday morning should speak with their bank in the first instance.
"They should also contact their bank if they have suffered any costs as a result of today's problems."
Matthew Robinson is co-founder of Hove-based translating service UK Techtrans, where the problem left his eight employees and 100 suppliers unpaid.
Many had to cancel holidays this weekend, he said.
Mr Robinson told Sky News earlier: "Today has been an absolute calamity.
"It affects our business in a bad way and I cannot get through to (HSBC) on their phones."
Nigel Moore, a sales representative in Exeter who has also had to cancel plans for a long weekend getaway, realised something was wrong when he checked his bank balance at around 5am.
He added that there was no communication from HSBC telling him what had happened or what he could do.
Mr Moore told Sky News: "I've got direct debits which are set to go on Tuesday and if I don't get paid I will incur bank charges as I will significantly be over my overdraft.
"This includes my child support payments to my ex-wife and I have not been informed as to whether I will be still liable for that.
"So not only will I have to sort out bills but have awkward conversations with the CSA (Child Support Agency)."
HSBC, which has 48 million customers in 72 countries, including 16.1 million in the UK, said the fault was in information used to process some payments from HSBC business customers, including payments to customers of other banks.
The Financial Conduct Authority said it would ensure HSBC did not leave people out of pocket.
The Bacs system deals with transactions worth around £50bn every day.
HSBC customers were advised to call 03457 404 404 for further information.
In June 600,000 payments failed to reach the accounts of RBS customers.
Andrew Tyrie MP, chairman of the Treasury Select Committee, said: "This appears to be yet another serious IT failure by one of the major clearing banks.
"It is increasingly clear that most, if not all, of these banks' IT payments systems need a good deal of investment, and there is a lot to put right.