The crime rate in England and Wales has fallen by an unexpected 15% to an estimated 7.5m offences, its lowest level since the official survey began 33 years ago.

The fall is one of the biggest in the history of the authoritative Crime Survey of England and Wales, and was driven by a 22% fall in violent crime, a 25% fall in some types of household theft, a 15% fall in vandalism and a 10% fall in car crime.

The murder rate in England and Wales also showed a slight fall in 2013, down to 551, and is now nearly 50% below the 2001-02 peak of 1,047, which included many of the victims of Harold Shipman.

The claim that England and Wales are now much safer than 20 years ago is reinforced by figures showing that even antisocial behaviour fell by 7% last year, extending a six-year decline.

The Office for National Statistics (ONS) said the 15% fall in the overall rate meant that crime had fallen by 25% since 2007-08 and by 60% since its peak level in 1995.

The second official measure of crime, the contested police-recorded crime figures, which have lost their national statistics status, showed a much smaller annual fall of 2% to 3.7m offences. Statisticians said this was possibly the result of a renewed focus on the quality of crime recording by the police following the political controversy over their integrity.

However, the police recorded crime figures reveal a continued upward pressure in specific crimes thought to be related to economic hardship, particularly shoplifting, which rose by 6% across England and Wales last year.

But this masked a growing north-south pattern, with the underlying figures showing rises in shoplifting of 20% in the West Midlands, 19% in Nottinghamshire and 16% on Merseyside. Increases in shoplifting were recorded in 34 out of the 43 police force areas.

The police figures also show the first fall for two years in smartphone street thefts, with the category of thefts from the person, which includes pickpocketing, falling by 2% last year.

The detailed police recorded crime figures also report a 17% rise in sexual offences including a 20% rise in rape to 19,214, the highest level for a decade.

The large rise in rapes and other sexual offences was partly due to increases in offences involving children, according to statisticians. The police figures record 13,090 sexual offences involving a child under the age of 13 in 2013, the highest reported total for a decade, and an increase of 32% on the previous 12 months. They include a 54% increase in rapes and sexual assaults on boys under 13 which rose from 1,775 to 2,727 last year. The number of sexual attacks on girls under 13 rose by 25% to 7,611 last year.

Statisticians said that the rises reflected similar recent figures from the National Society for the Prevention of Cruelty to Children, which attributed some of this increase to the impact of the Jimmy Savile case. They said that media coverage of Savile and the police investigation into historical sex crimes, Operation Yewtree, had prompted victims to come forward.

The 2013 crime figures are the first full-year data after the Savile disclosures, and the "Yewtree effect" is starting to decline, statisticians say. While allegations relating to current offences rather than historical allegations accounted for only 21% of the increase in the crime figures six months ago, they now account for 50% of the increase in this latest set.

The detailed crime figures also show a 25% rise in fraud to 207,252 recorded by Action Fraud, a new central organisation which has taken over the recording of fraud in all police force areas. Much of it is online fraud, data for which was not being captured by individual police forces before.

But the overall picture shows a 15% fall in crime across nearly all other categories.

The detailed figures show not only a continued decline in the murder rate but robberies down 12%, gun crime down 6% and knife crime down 4%. Household burglaries, once the main crime concern in the 1980s and 1990s, show a further 4% fall on the crime survey.

Drug offences were also down by 5% but 171,000 people are still being penalised for possession of drugs, mainly cannabis.

There is no consensus among criminologists about the key factors driving the sustained fall in crime. Earlier this week Cardiff University researchers highlighted the decline in binge drinking and rising alcohol prices as a factor, but competing theories include links to the state of the economy and the removal of lead in petrol.

Statisticians said that the difference between the 15% fall estimated by the survey and the much smaller 2% fall on the police recorded figures partly reflected the renewed focus on improving their quality. They pointed to rises in recorded violent crime figures of 26% in Gwent and 25% in Kent – the two forces where the controversy over "fiddled figures" was most intense – as evidence of a correction in recording methods taking place.

Norman Baker, the crime prevention minister, said the figures showed clear evidence that the government's programme of police reform was working.

He said: "The government has a strong record on reinforcing the independence and accountability of the statistics. We asked Her Majesty's Inspectorate of Constabulary last June to carry out an audit of the quality of crime recording in every police force, and the home secretary has written to chief constables emphasising that the police must ensure that crimes are recorded accurately and honestly."

But Jon Collins of the Police Foundation said the government should be wary of resting on its laurels. "While some crimes – such as burglary and car crime – are clearly not the problem they once were, it's possible that the official crime figures are just not picking up the extent to which new opportunities for crime have emerged, particularly online," he said.

He added: "Significant increases in levels of fraud, while likely to be at least in part a product of changes in reporting and recording practice, are of particular concern within this context. In welcoming falling crime rates, it's important not to be blind to new and emerging challenges."