The National Crime Agency is warning computer users they have two weeks to protect against a "powerful computer attack".
It comes as US officials held a press conference accusing a Russian hacker of masterminding the scam and raking in £60m.
Two pieces of malware software known as GOZeuS and CryptoLocker are at the centre of the alert.
People are being warned to make sure their security software is installed and up to date, and to run scans to check for any problems.
Important files should also be backed up, said the UK's National Crime Agency (NCA).
The malware typically infects a computer via attachments or links in emails.
"(They) may look like they have been sent by genuine contacts and may purport to carry invoices, voicemail messages, or any file made to look innocuous," the NCA warned.
"These emails are generated by other victims' computers, who do not realise they are infected, and are used to send mass emails creating more victims."
The agency said GOZeuS (also known as P2PZeuS) was responsible for hundreds of millions of pounds of fraud globally.
If a user clicks on an infected link or attachment, the malware silently monitors activity and tries to capture any private information, such as banking details.
Sky's Technology Correspondent Tom Cheshire said: "We should all be concerned. It goes specifically after financial information, and if that is over a certain threshold it starts stealing it, very silently without you necessarily noticing."
The second threat comes from the Cryptolocker malware which can lock a user out of their file, for example photos or text documents, until a "ransom" of several hundred pounds is paid.
"Recent intelligence has suggested that more than 15,500 computers in the UK are currently infected, with many more potentially at risk," said the NCA.
FBI action in the US had weakened the network of affected computers, said the NCA, "meaning that action taken now to strengthen online safety can be particularly effective".
Thirty-year-old Russian Evgeniy Bogachev is the alleged leader of the gang behind the attacks, FBI executive assistant director Robert Anderson told reporters in Washington DC.
"GameOver Zeus is the most sophisticated botnet the FBI and our allies have ever attempted to disrupt," Mr Anderson said.
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