Crime in England and Wales is at its lowest level since 1981 after a record 16% fall in the past 12 months, according to the Office for National Statistics.

The authoritative crime survey shows a decline in most offences, including a 23% fall in violent crime, a 20% drop in criminal damage and a 12% decline in theft.

The survey estimates that there were 7.1m crimes in the 12 months to June 2014.

However, separate police recorded crime figures – which no longer carry the national statistics gold badge – show a 21% rise in sexual offences, including a 29% increase in rape. The figure of 22,116 attacks is the highest for at least 10 years. The data also shows an 8% rise in fraud and a 5% increase in shoplifting.

ONS statisticians say the police recorded figures show no overall change from the previous year, with 3.7m offences recorded.

The statisticians put the increase in fraud and an 11% rise in violence against the person down to increased police compliance with national standards in recording crime. However, they said the 5% rise in shoplifting was probably the result of a genuine increase in crime rather than a change in recording practice.

The detailed figures show that rapes carried out at knifepoint rose by 48% in the past year from 199 to 294, while sexual assaults by knifepoint were up 22% from 91 to 111.

ONS statisticians said the 21% rise in rape and other sexual offences was driven by an increase in the willingness of victims to report the attacks to police, as well as an improvement in police recording practices.

Separate Home Office figures published on Thursday show that hate crimes in England and Wales rose 5% to 44,480 in 2013/14. Race hate crimes rose by 4% to 37,484 and religious hate crimes were up 45% to 2,273 offences. Statisticians say most of the increase in race and religious hate crimes came in the aftermath of the murder of the soldier Lee Rigby in Woolwich. More than one motivating factor was recorded for many of the incidents.

The ONS statisticians added that the 16% overall fall in crime levels on the authoritative crime survey of England and Wales represented a drop of about 1.3m offences. They said a separate estimate of 300,000 plastic card fraud offences online not captured by the official crime survey would have reduced that fall to about 1m fewer crimes.

Norman Baker, the crime prevention minister, said the latest set of quarterly crime figures showed there were positive signs that police recording of crime was improving, and that more victims of crimes such as sexual offences and fraud were coming forward.

“It is vital that police recorded crime statistics are as robust as they can be. That is why the home secretary asked Her Majesty’s Inspectorate of Constabulary to carry out a detailed investigation of recording practices in all 43 forces. HMIC’s final report is due shortly and we expect chief constables and police and crime commissioners to act on its recommendations.”