A fifth of people fear net crime the most, the report says
The Get Safe Online study released by the government found 21% of respondents felt most at risk from net crime, while 16% worried most about being burgled.
A BBC investigation into net-based attacks on Windows PCs found they could happen as much as every 15 minutes.
At least every hour, an unprotected PC set up as a honeypot logged a malicious attack that could render it unusable or make it access other machines.
Similar so-called "honeypot" computers have become indispensable to computer security experts monitoring online crime in recent years.
The government's study also found fears of online crime ran so deep some people were being put off using the internet altogether.
But Get Safe Online campaign boss Tony Neate said people only needed to take simple steps to avoid almost all types of net dangers.
The survey was released as the Get Safe Online campaign gets a re-launch and embarks on a national tour that aims to tell people about good web browsing habits.
As well as highlighting fears, the survey also indicates the net is becoming an increasingly important part of many Britons' lives.
Mr Neate, campaign managing director, said 57% of UK households had a internet connection and 69% of those were linked up via broadband.
In the first six months of 2006, British shoppers spent more than £13bn online, the survey found, and 52% of Britons questioned did their banking online.
But hand-in-hand with this went worries about the dangers greater net use posed, said Mr Neate.
He said 18% of those questioned said they would not shop online because they were concerned about becoming a victim of net crime.
The survey also found that many people are still not taking basic steps to protect themselves when they use a PC to go online.
The survey found 17% of people had no anti-virus software and 22% had no firewall. A further 23% said they had opened an e-mail attachment that came from an unknown source.
Mr Neate said the numbers of people visiting the Get Safe Online website and how long they stayed was an indicator the message was starting to get through.
Since the October 2005 launch more than 750,000 people had visited the website, he said.
He added that people should regard their PC like their car and take similar steps to keep it in good working order and safe from thieves.
"It's about crime prevention and awareness," he said. "Take some simple precautions and people are going to be safe."