The Office for National Statistics said preliminary research indicated there were 5.1 million incidents of fraud, with 3.8 million adult victims in England and Wales in the 12 months prior to being interviewed between May and August.
In addition, there were an estimated 2.5 million incidents of cyber crime falling under the Computer Misuse Act.
The data from the Crime Survey of England and Wales also revealed that overall crime has fallen by 8% from last year with an estimated 6.5 million offences.
It is the lowest level since the survey began in 1981.
Separate police recorded crime figures, which are compiled in a different way, showed an increased of 5% with 4.3 million incidents.
The estimates for fraud and cyber crime are significantly higher than those suggested by the police recorded figures, according to the Office for National Statistics (ONS).
“There are a number of reasons why the CSEW estimate is so much higher than the figures recorded by the police,” the survey stated.
“The profile of cases covered by the CSEW cover the full spectrum of harm or loss.
“Reporting rates are likely to be lower in cases where there is low or no harm, but merely inconvenience, to the victim.”
The latest police figures show just under 600,000 fraud offences were reported to the National Fraud Intelligence Bureau (NFIB), a rise of 9% compared with the previous year.
More than half of fraud and cyber crime victims suffered financial loss, the survey found.
Of that number, 78% received financial compensation and 62% were fully reimbursed.
The most common cyber crimes, offences committed under the Computer Misuse Act, were where the victim’s device was infected by a virus.
It also includes people’s emails or social media accounts being hacked.
The CSEW, published quarterly by the Office for National Statistics, reflects experience of crime and is separate from police-recorded crime figures which only show how many offences were reported.
The new figures on fraud and cyber crimes do not show if the occurrence of these offences is going up or down, according to the ONS.
“It is important to recognise that these new data are not simply uncovering new crimes, but finding better ways of capturing existing crime that has not been measured well in the past,” the survey said.
“However, it is not possible to say whether these new figures represent an increase or decrease compared with earlier levels.”
The number of frauds reported to the National Fraud Intelligence Bureau increased by 9% with around 600,000 offences.
ONS spokesman Glen Watson said: “Since taking over the Crime Survey for England and Wales in 2012, ONS has been working towards improving the coverage of crime statistics and today publishes its first estimates of fraud and cyber-crime committed against the household population.
“We are at the forefront of international efforts to bring official crime statistics into the digital age.
“Although we estimate that there were more than seven million fraud and computer misuse incidents in the past year, this does not necessarily imply a recent rise in crime as the new measures bring into scope a large volume of offences not previously included in the Crime Survey for England and Wales.
“Furthermore, these new estimates should be seen in the context of a reduction over the past 20 years in the more traditional forms of crime, from 19 million incidents a year in 1995 to under 7 million a year today.”
Crime Minister Mike Penning insisted crime rates are continually dropping because of police reforms.
“Crime is falling and it is also changing, and we are committed to tackling fraud and cyber crime,” he added.
“This is not a new threat and the Government has been working to get ahead of the game.
“Since 2010, we have created the National Crime Agency, invested £860 million in the National Cyber Security Programme and established Action Fraud to support police by identifying the links between complex scams.”
He claimed the rise in violent and sexual crimes being reported to the police was due to changes in how offences are recorded.
“The Office for National Statistics has been clear that this rise reflects improvements in recording practice, rather than an increase in itself and this is something we welcome,” he continued.
“Tackling these horrific crimes is a priority, and we have introduced new laws that mean anyone caught in possession of a knife for a second time will now face a mandatory minimum sentence in prison.”
On average one in 12 adults is a victim of fraud and one in 22 is a victim of cyber fraud, the figures show.
The survey also revealed the number of sexual offences, including rape, reported to the police rose by 41% from last year and is at the highest level since comparable records began in 2002.
There was a 25% rise in violence against the person reported to the police, including in the most serious categories resulting in injury.