Asian hackers are targeting UK businesses and government departments on an unprecedented scale, according to the Financial Times.
Nearly 300 government departments and businesses vital to British infrastructure have been subjected to an attack for several months, it said.
The UK's National Infrastructure Security Co-ordination Centre (NISCC) has urged businesses to stay alert.
The attacks, which also target the US, seem mainly to be coming from Asia.
According to the government-backed NISCC, the aim appears to be to steal commercially and economically valuable information.
The attacks are contained in so-called Trojan horse viruses, which are small programs hidden inside attachments to Emails. These Emails have a subject line, which makes them look like normal correspondence.
The Emails appear to come from people known to the recipient.
Once the Email attachment is opened, the Trojan enables a hacker to take control of the recipient's PC.
Recent reports suggest that hackers are getting more sophisticated and can make viruses and other harmful software mutate so quickly that anti-virus software has difficulty keeping up.
The UK's NISCC and National Hi-Tech Crime Unit are working with the authorities in a number of Asian countries to identify and shutdown the Internet addresses the attacks are coming from.
The countries involved have so far not been named.