It is not difficult to find some horror story about a crime perpetrated by a foreigner in Britain. Indeed, some parts of the media seem to specialise in it. So it is good to have the wherewithal to stand back and consider the wider context. That was provided to the Home Secretary yesterday by a wide-ranging study from the Association of Chief Police Officers on crime levels among immigrants to the UK from eastern Europe in recent years. The report found that, contrary to the alarmist headlines, the offending rates among Polish, Slovak, Lithuanian, Romanian and Bulgarian incomers are pretty much in line with the rest of the population. Another myth bites the dust.

There are problems, of course. It found that the rapid influx of foreign workers had caused blips both in types of crimes and in their varying geographical impact. Poles, who make up than half of the incomers, have a higher rate of drink-driving offences. There have been Romanian gangs, particularly in London, using children for petty robberies in a way which would have been unsurprising to Charles Dickens but which particularly shocks modern English sensibilities. And there have been increases in sex trafficking, worker exploitation and other forms of modern-day slavery, among Britain's new eastern European communities.

Some areas suffer more than others, in ways which upset our stereotypes. London is no longer the top destination for migrant workers. Most of the mass arrival has been absorbed into farm work in areas like south-west England and East Anglia – parts of the country unused to large-scale immigration. Which is why last year it was the chief constable of Cambridgeshire who sparked controversy by claiming the sudden inflow of east Europeans had led to community tensions.

But this new report contextualises all that. Part of the increased burden placed upon police in such areas is a significant rise in the budget for interpreters, not because the eastern Europeans are all offenders but because they are also victims and witnesses of crime. It is also because, in the local psyche, rumour often trumps mere fact; prejudices, resentments and misunderstandings fuel tensions – which police have had to be proactive in resolving and which make investigations more complex.

The cold facts are that Britain has accommodated this huge influx with comparatively few real, as distinct from perceived, problems – and crime has actually fallen in England and Wales by 9 per cent in the past recorded year. The evidence just does not support wild theories of a massive crime-wave generated through migration.

The myths around immigration crumble when exposed to the light of day. Few of the incomers sponge on the state; as many as 97 per cent of registered immigrant workers have full-time jobs; the number on benefits is very low. Immigration is good for us.Migrants do jobs that many Britons turn down. They perform vital tasks in the public services. The economy grows faster because of their contribution. Inflation and interest rates are kept down.

Sainsbury's have even suggested that the strong work-ethic of foreign-born workers rubs off on the British-born staff. And because, as yesterday's police report pointed out, many migrant workers are young professionals with qualifications who come here to earn money and then return home, the tax they pay helps to defuse the UK's pensions time-bomb because they are not staying to grow old and draw pensions themselves. Then there are all the benefits of innovation and diversity and other fruits of immigration that cannot be measured.

All of this does not, of course, suit those politicians who see advantage in demonising the foreigner. But then facts rarely do.