A backlog of payments - including wages - that were blocked by an IT problem on Sunday has yet to be cleared, three days on from the glitch.
Some bank customers have spoken of their frustration that payments had not yet reached their destination.
The Faster Payments system should see money moved within two hours.
A spokesman for the service said "good progress" was being made to clear the backlog and customers should not be left out of pocket.
However, he refused to predict when the outstanding payments would be made.
The UK's Faster Payments system is one of the major pillars of the UK's infrastructure for moving money.
Payments, and transfers between bank accounts, using the system should reach their destination within two hours and often clear instantaneously.
A fault occurred between 13:00 and 17:30 BST on Sunday, at a time when a total of 769,480 payments were being processed.
A fraction of those have still to be completed, but that is causing frustration for some people who have not been paid or have tried, for example, to transfer money to builders.
@AskHalifaxBank I was sent my wages by faster pay on Sunday. Still no sign of it after three days. Any update?— Sophie Southwell (@sophiesouthwell) July 11, 2018
@santanderukhelp @BBCBreaking 4th day of waiting for £2k+ to clear. We had building works completed last week, paid builders on Sunday, they still have no money. They are now putting pressure on to be pair, because their suppliers need paying. Absolute farce. 1/2— Cap'n Matt (@pilotstenen) July 11, 2018
"Anyone who has been affected by a payment that has not been received should speak to their own bank, building society or other provider. No-one who has been affected by this issue will be left out of pocket," a spokesman for Faster Payments said.
He said that the backlog had been created by some payments being rejected during the shutdown.
These payments were being checked manually to ensure that there would not be a double payment if they were resubmitted to the system.