Most of the attacks involved viruses, spyware or malware, the Cyber Security Breaches Survey says. A quarter of large firms experiencing a cyber breach did so at least once a month.
Digital Economy Minister Ed Vaizey said it was "absolutely crucial businesses are secure and can protect data".
In some cases the internet-linked attacks cost millions of pounds.
The survey's results have been released alongside the government's Cyber Governance Health Check, launched following the TalkTalk cyber attack in October last year.
The phone and broadband provider, which has over four million UK customers, said some of their banking details and personal information could have been accessed in the breach.
In light of these surveys, businesses are now being urged to protect themselves better.
Mr Vaizey said: "The UK is a world-leading digital economy and this government has made cyber security a top priority.
"Too many firms are losing money, data and consumer confidence with the vast number of cyber attacks. It's absolutely crucial businesses are secure and can protect data."
The survey also suggested seven out of 10 attacks could have been prevented, and added that only a fifth of businesses understand the dangers of sharing information with third parties.
The government is investing Â£1.9bn over the next five years to tackle and prevent cyber crime, and a new National Cyber Security Centre will offer security support.
Also, a national cyber security strategy will be published later this year, setting out proposals to improve online security for the government, among businesses and for consumers.
Two-thirds of big UK businesses have been hit by a cyber attack in the past year, according to government research.