More than 1.1 million or 7% of women and 720,000 or 4% of men have been victims of some kind of domestic abuse in the past year, official crime figures reveal.

The full scale of the hidden world of sexual assault, family abuse and stalking is revealed in official figures that show that nearly 5 million women or 30% of the adult female population have experienced some form of domestic abuse since age 16.

The latest figures from the Crime Survey for England and Wales also reveal that there were an estimated 406,000 victims of sexual assaults last year and nearly one million victims of stalkers. More than two-thirds of these were women.

The annual survey of people's experience of crime also reveals that a startling 10% of the public think that it is "mostly or sometimes" acceptable to hit or slap their partner in response to them having an affair. This rises to 16% of older teenagers, with little difference in attitude between men and women.

This previously hidden scale of domestic abuse in England and Wales has been revealed as headline rates of violence continue to fall.

The murder rate in England and Wales stood at 551 homicides recorded by the police in 2012/13. This is a slight increase since 2011/12, when 530 homicides were recorded, but the Office for National Statistics (ONS) said these continue a general downward trend and are the lowest levels since 1989, when there were 521 homicides.

The most likely murder victim is a child of either sex under the age of 12 months. Men account for two-thirds of murder victims and are most likely to have been killed by a friend or acquaintance, while women are far more likely to be killed by a current or former partner.

The statisticians point out that more people were killed as a result of falls (3,790), intentional self-harm (3,671), and transport accidents (1,662) than were murdered in the last year. But only 193 people died in fires and 196 drowned.

The decline in the murder rate was more than matched by further 15% falls last year in both gun crime and knife crime. Gun crime fell to 8,135 offences and 29 people were killed in shootings, the lowest number since 1980. Knife crime fell to 26,340. This was twice the 7% fall in violent crime recorded by the police in 2012/13.

The statisticians say the chance of becoming a victim of violent crime in England and Wales is now less than half what it was when violent crime was at its peak in 1995. Violent crime against adults in England and Wales has fallen from an estimated 4.2m incidents a year in 1995 to 1.9m in 2012/13, according to the crime survey.

The ONS said that while the official "badge" of national statistics had been withdrawn from the police recorded crime figures, the crime survey results continued to meet that standard and that it would continue to publish and provide commentary on both sets of figures.

The statisticians discounted a 17% rise in the latest police-recorded crime figures for sexual offences, attributing it to a 'Yewtree effect' - increased reporting of alleged sexual abuse in the wake of publicity about Jimmy Savile. They say a decline in sexual offences as measured by the official crime survey reinforces this conclusion.

The crime prevention minister, Norman Baker, said it was good to see violent crime continuing to fall: "The independent crime survey for England and Wales for 2012/13 shows the number of violent crimes at its lowest level since 1981. Police recorded crime statistics show firearms offences fell by 15% in the last financial year, knife crimes dropped by 15% and there were 13% fewer robberies, but we want to do even better," he said.

"We are continuing to work to stamp out gang violence, tackle domestic abuse and protect vulnerable women and girls from sexual exploitation."