HSBC said it was working to resolve the glitch as quickly as possible and apologised to those affected. It has contacted the Bank of England.
The Financial Conduct Authority (FCA) has also been made aware and said it would ensure the bank took steps to help those left at a disadvantage.
The problem is thought to have affected payments made from HSBC accounts using the national Bacs payments system but not those from other banks.
But it does mean that customers of those other banks have not had money paid to them that they would have expected to receive.
The scale of the transactions and number of customers involved is not yet known. HSBC has 16.1 million customers in the UK.
Alan Charlesworth, managing director of insurance and legal recruiter IPS Group, took to Twitter to complain: “None of my staff have been paid. HSBC when will this be sorted?”
Another Twitter user wrote: “HSBC. None of my staff have been paid. Cannot get through to them on the phone. Absolute shambles of a bank! Extremely poor performance.
“I trust you are going to reimburse my employees that will incur late payment fees due to your Bacs payments failure.”
Also on Twitter, one user wrote: “Bacs payment system down on payday and before Bank Holiday. Lovely.”
Lydia Smith tweeted: “HSBC UK where’s my money? I didn’t get paid my wages today and I have bills to pay.”
HSBC said in a statement: “We are aware that some customers have not received expected credits today. We apologise for any inconvenience caused and are working hard to resolve the issue as quickly as possible.”
Bacs processes transactions worth up to around £50 billion every day and is seen as critical to the functioning of the UK financial system.
It said: “Bacs is aware of an isolated issue affecting one of its member organisations. The Bacs system is operating as normal and we are currently working with our partners to help resolve this as quickly as possible.”
The Bank of England said: “We are in contact with HSBC regarding their recent IT issue. We will be working closely with HSBC as it resolves the problem.”
An FCA spokeswoman said: “The FCA is in contact with HSBC regarding the issue.
“We will be working closely with the firm as it resolves the problem and to ensure there are steps in place to help consumers who are affected.”