Crime in England and Wales fell sharply last year with an 8% drop recorded on police figures and a 5% reduction according to the official crime survey, the Office for National Statistics has said.

Statisticians say the crime rate has halved since it peaked in 1995 and appears to be at its lowest level for more than 30 years. The official 2012 statistics show that all the main categories of crime recorded by the police fell, with violence down 6%, robbery down 13% and burglary down 9%. The murder rate also continued to fall in 2012, down 4% from 577 to 552 homicides. Knife crime fell by 16%, including a fall in the number or rapes involving a knife from 246 to 191.

There was a 3% reduction in the number of sexual offences, but the ONS said the effect of Operation Yewtree, the inquiry launched in the wake of the Jimmy Savile scandal, might mean more people coming forward to report historical sex abuse allegations.

The only category on the police figures to see an increase was theft from person, which rose 8% to 107,471 incidents. Police said the increase, which was concentrated in London, was driven by a rising number of mobile phone thefts, sometimes by youths on bikes.

The crime survey for England and Wales, which interviews more than 40,000 people about their experience of crime, estimates there were 8.9m crimes in 2012. This is the lowest level since the survey began in 1981 when it estimated there were 11m crimes. The police figures recorded 3.7m offences, which is the lowest on this measure since 1989 although changes in counting rules make comparisons more difficult.

The official statisticians say results from the more reliable official crime survey for England and Wales show that crime rose steadily from 1981 to 1991 before peaking in 1995. "Subsequently, the crime survey for England and Wales showed marked falls up to the 2004-05 survey. Since then the rate of reduction has slowed with some fluctuation from year to year."

Deputy Chief Constable Jeff Farrar, of the Association of Chief Police Officers, said the falls reflected the efforts of the police to protect communities. "The percentage of people who believe that crime is increasing at the local level has almost halved in the last decade," he said.

"But we cannot be complacent and while overall these results are positive the police service will need to adapt and innovate to continue bringing down crime as their budgets decrease."

The crime prevention minister, Jeremy Browne, said it was particularly encouraging that the downward trend had been replicated across every police force in England and Wales. "They have shown an impressive ability to accommodate necessary budget reductions while still cutting crime," he said.

The fall in crime was not matched by further reductions in concern about anti-social behaviour which remained static with 14% of adults saying it was at a high level in their area.

The crime survey does, however, show declining levels of concern about teenagers hanging round streets (down from 25% to 23%), public drunkeness or rowdiness (down from 24% to 22%) and vandalism and graffiti (21% to 20%). The sharpest long-term decline has been concern over abandoned or burnt-out cars which peaked at 23% and is now down to 4%.