Crime levels are continuing to fall steadily, according to the latest statistics, with offences recorded by the police in England and Wales dropping by 5% over the past year.

Latest responses to the annual crime survey – the other official measure of offending, based on interviews rather than police figures - show an even greater decline of 7%. to a level that is less than half its peak in 1995.

Within that overall pattern, however, there are significant exceptions: muggings have risen sharply by 8% and sexual offences are up by 9% over the past 12 months. Fraud is up 21%.

The increases in sex offences may be due, according to the Office for National Statistics, to a "Yewtree effect" following the police operation investigating allegations against Jimmy Savile and other historic sex offences. The publicity is thought to have encouraged more victims to come forward.

The rise in muggings, which comes under the category of "theft from the person", is likely to reflect the fact that more people are carrying expensive mobile phones and electronic gadgets, which makes them easy street targets.

The increase in fraud is partially attributed to more centralised recording of dishonesty offences by the police. In the year ending June 2013, 230,335 fraud offences were recorded.

The figures show that there were 3.7m crimes recorded by police to the year ending June 2013, making it the lowest level since the current method of recording offences was begun in 2002/3.

The higher figure of 8.5m crimes, detailed in the Crime Survey for England and Wales from the past year, is the lowest level since the series of interviews began in 1981. The survey traditionally produces different statistics from police figures because not all crimes are reported to police.

The survey showed that as many as 800,000 children aged between 10 and 15 experienced crimes.

There were an additional 1m offences dealt with by the courts in the year ending March 2013 (the latest period for which figures are available), which are not included in the police recorded crime figures. These cover less serious crimes such as speeding offences, which are dealt with by magistrates courts.

Welcoming new crime statistics for the year to June 2013, the crime prevention minister, Norman Baker said: "Police reform is working and crime is falling. Recorded crime has dropped yet again, by more than 10% under the coalition government and the crime survey says that crime has more than halved since its peak in 1995.

"This is really positive news. Forces are rising to the challenge of making savings while cutting crime and delivering a better service to the public.

"England and Wales are safer than they have been for decades but we will continue to deliver measures which keep pace with the changing nature of crime and improve our ability to combat emerging issues.

"That is why we have recently launched the National Crime Agency to tackle the growing threat of serious and organised criminality. The agency also incorporates the new National Cyber Crime Unit to relentlessly pursue cyber-criminals."

Max Chambers, the head of crime and justice, at the Policy Exchange thinktank, said: "Whether you believe it's as the result of an ageing population, better policing and prevention, or the impact of the internet, there is little doubt that Britain is becoming a safer place to live, do business and raise a family.

"While the latest figures show that the police have been able to cut crime substantially even with fewer resources, they must now redouble their efforts to tackle the hard core of prolific offenders who commit offences that can often disproportionately hit the poor and the vulnerable."

Jon Collins, the deputy director of the Police Foundation, an independent policing thinktank, said: "Nobody knows exactly why some, but not all, forms of crime captured in the official statistics have fallen so substantially and continue to fall, particularly given the current economic circumstances. It is likely to be the product of a number of related factors, including improved security and better policing.

"While crimes such as burglary and car crime are clearly not the problem that they once were, it's possible that the official crime figures are just not picking up the extent to which new opportunities for crimes like fraud and counterfeiting have emerged, particularly online."