There were an estimated 3.6 million cases of fraud and two million computer misuse offences in a year, according to an official survey.
The Crime Survey for England and Wales included the offences for the first time in its annual report, which covered the year to September.
Separate figures recorded by police showed an 8% rise in offences overall.
The Office for National Statistics said crime recording improvements meant the police figures could not reveal trends.
'Crime has changed'
John Flatley, from the ONS, said: "In the past, burglary and theft of vehicles were the high-volume crimes driving trends but their numbers have fallen substantially since then.
"When the crime survey started [35 years ago], fraud was not considered a significant threat and the internet had yet to be invented.
"Today's figures demonstrate how crime has changed, with fraud now the most commonly experienced offence."
Sir Tom Winsor, the Chief Inspector of Constabulary for England and Wales, told the You and Yours programme on BBC Radio 4 that many frauds went undetected and a great deal never got reported to the police.
"The amount of fraud that is taking place now is probably in epidemic proportions," he added. "The police are having to work very, very hard to keep up with even the ones they know about.
"The capability at police forces is quite skeletal and that needs to change and change a great deal."
The National Police Chiefs' Council lead for crime and incident recording, Chief Constable Jeff Farrar, said forces were working with the Home Office, police and crime commissioners, and industry experts to develop new tactics to fight cybercrime.
"The ability to commit crime online demonstrates the need for policing to adapt and transform to tackle these cyber challenges," he said.
Cyber and fraud: What is being counted?