Internet users are being warned about cold-callers who offer to fix viruses but then install software to steal personal information.
Campaign group Get Safe Online said a quarter of people it had questioned had received such calls, many suspected to have been from organised crime gangs.
Some gangs, employing up to 400 people, are known to set up their own call centres to target people en masse.
Internet users are also urged to be wary of pop-ups offering virus checks.
Earlier this year, search engine giant Google warned it had discovered massive amounts of malicious fake anti-virus software.
The UK warning on such software comes from Get Safe Online, which is backed by the government, police forces and major businesses with a stake in internet security.
It says it has charted a growth in two related scams designed to trick people into installing fake anti-virus software as a means of harvesting personal information such as credit card details.
Some of the scams involve pop-up windows claiming that the computer has been infected.
These "scareware" approaches encourage users to click through to a site hosting malicious or useless software that acts as a front for gathering personal information. Most of the time, the software appears almost identical to professional anti-virus products.
In other cases, gangs have set up call centres in eastern Europe or Asia and cold-call UK phone numbers attempting to find people to con.
In both cases, information gathered from the identity thefts can be used by gangs or sold on to other criminals through online market places.
Investigators from the UK's Serious and Organised Crime Agency (Soca) e-crime unit attempt to track scams back to the source gangs who have set them up.
Sharon Lemon, deputy director of Soca, said: "In recent cases, we have seen gangs employing 300 to 400 people to run their operations and using call centre-scale set ups to target victims en masse.
"They can also be paying out as much as $150,000 (£92,000) a month to individual webmasters who are unwittingly advertising their fake software - this level of investment from criminals indicates that the returns are much heftier than this."
Tony Neate, head of Get Safe Online, told the BBC that one operation in eastern Europe turned over £4.5m in a year.
He said: "This is big business, and it's preying on people's fears of the internet. The internet is a great place but when somebody phones you up and tells you you have a virus on your machine, you will start to panic."
Dr Emily Finch, a criminologist at the University of Surrey, said: "The general public is more internet security-aware than it was five years ago. Malicious anti-virus scams are an indication that criminals are now tapping into this.
"Rather than exploiting our ignorance - the basic premise of common scams such as phishing - they are actively using our knowledge and fear of online threats to their advantage."
Get Safe Online's annual report says its research suggests a third of UK internet users are still victims of viruses, despite steady improvements in security. More than a fifth said they had suffered identify fraud.
ICM interviewed 1,520 computer-using adults during October for the survey.
BBC News website readers have been reacting to this story with their experiences of unsolicited calls. Here is a selection of their comments:
I have received this type of call and also the pop-ups. The pop-ups are the most difficult because they prey on the fear of being infected. The software should never be downloaded or activated. One give-away on the telephone calls is that they say they are calling about your 'Windows computer' - of course Windows is an operating system, not a computer. I have had two such calls and the caller got more pressing when I pointed that out to him. He said, "well that is up to you sir but your computer is infected." Raymond, Milton Keynes
"Richard" has telephoned me a couple of times from India informing me that I was on the computer - which was true - and that a virus had been detected. I informed him my husband was a computer engineer and there was no possibility of this being the case. Gillian, Hereford
I too have received such calls. The golden rule as far as I'm concerned is to not entertain any unsolicited contact. That includes phone calls, pop-ups and visitors to your home. If you didn't actively request contact, then simply ignore it. They'll quickly move on. Darren, Barnsley
We have received a large number of telephone calls from people purporting to be representing Microsoft and telling both my wife and I (who have both answered calls at different times from these individuals) that they have noticed that our computer has a virus, and offering to talk us through the removal process. In all cases we put the phone down. Ian, Newcastle
I received a call a few months ago saying that there was a problem with my PC. As I have a Mac instead, I was immediately suspicious so I said "this is a scam" and put the phone down. Kate, Leeds