HALF of the foreign-language section in Corby’s public library is taken up with Polish books. “Alicja w Krainie Czarów” (“Alice’s Adventures in Wonderland”) sits near “Agresor”, a translation of a military potboiler. A decade ago this town in the East Midlands had hardly any east European bookworms to cater to. As in many other places, its residents have been surprised, and at times perturbed, by what has happened since.

Poles, who have been able to live and work in Britain since their country joined the European Union in 2004, have already become the second largest foreign-born group, after Indians. The 2011 census counted 579,000, a tenfold increase from a decade earlier. Many more have come and gone: since 2002 almost 1.2m Poles have been issued with National Insurance numbers. But that still leaves a lot of settlers. In 2012 Polish women gave birth to 21,156 children, more than any other group apart from native Britons. They have ventured to rural market towns and small cities that rarely see foreigners.

Poles and other east Europeans have also become political footballs—with almost all national politicians playing in the same, hostile, team. Jack Straw, once Labour’s home secretary, calls the decision by his party to grant them free access to Britain a “spectacular mistake”. Priti Patel, a Conservative MP, says (with many others) that they are straining public services to breaking point.

Politicians are now applying the conclusions they have drawn from the Polish surge to a new group of migrants. Fearing an influx of feckless Bulgarians and Romanians, who will be allowed free access to Britain and other EU countries from January 1st, the coalition government is tightening access to welfare. David Cameron, the prime minister, insists that Britain will not see a repeat of “the Polish situation”. Bulgarians and Romanians are already attracting more press coverage—mostly hostile—than Poles ever have (see chart).

But what, really, is the Polish situation? It is much more encouraging than politicians imply. Poles and migrants from other new EU member states have been readily absorbed into Britain’s labour market. They are tolerated, even welcomed, locally. The huge imbalance between local experience and national conviction has implications for next year’s migrants. Poles have mostly ended up in fast-growing bits of the country. Many live in London. Corby is one of the few places in NIMBYish Britain that welcomes house-building. Tom Beattie, the council leader, wants its population to double by 2030. Southampton, another city with lots of immigrants from eastern Europe, has gone from being an ageing city with declining skills to a young one with great aspirations, says John Denham, one of the city’s MPs. Marco Cereste, the Tory leader of the council in Peterborough, another popular destination for migrants, says his magazine-distribution company was turning away business ten years ago for a lack of workers. Not any more. And Poles are moving beyond menial, letterbox-stuffing work. Britain got younger and better-educated Poles than Germany or America. Many are overqualified for their jobs, and ought to move into more appropriate ones as their English and social networks become stronger. Some are already doing so. In the West Midlands, Polish entrepreneurs at first set up restaurants and construction firms. But later migrants, many of them women, built design firms and marketing agencies. A couple run bakeries big enough to supply leading supermarkets. Websites that once simply provided information for new arrivals have become commercial ventures that charge for access and advertising. Ilona Korzeniowska, editor of the Polish Express, a London-based newspaper, suggests Bulgarians and Romanians may fill jobs no longer of interest to Poles.

Parts of England and Wales with many east European migrants have seen a drop in property crime and no increase in violence, according to researchers at the LSE and University College London. Recorded crime and anti-social behaviour in Corby has fallen by more than half since 2006; in the rest of England and Wales it is down by about a third. The proportion of the town’s residents worrying about anti-social behaviour has plummeted from 56% to just 8%. A rise in knife crime in Cambridgeshire was mostly a result of workers taking home blades they used to harvest fruit and vegetables, unaware that carrying them was illegal, says Julie Spence, the area’s chief constable from 2005 to 2010.

Schools are under more pressure. Between 2008 and 2012 the number of Polish pupils in England doubled, to 54,000. Peterborough’s school population has swelled by 4,000 since 2008. Places are so scarce that some parents have four children in four different schools. But the new arrivals do not seem to be making it harder to learn. In Peterborough the share of pupils getting five good GCSEs, the exams taken at 16, rose from 37.2% in 2008 to 57.7% this year, just below the national average of 60.2%. Polish Saturday schools are springing up in Peterborough and elsewhere.

Other public services have been strained less. Corby has spent less than £300 ($490) on translation services thus far this financial year. Margot Parker, who stood as the UK Independence Party’s candidate in the town’s by-election last year, says its health services are struggling. If so, that would be unusual: east European immigrants tend to use the NHS much less than Britons. Few Poles there or in Southampton live in public-sector housing or are waiting for it; they prefer to rent privately. Nor do many claim unemployment benefits: in 2011 the number of jobless Poles in Britain was under 20,000.

The next wave

Dispiritingly, both for Poles and for those who will follow them to Britain, these local successes do not register nationally. Bulgarians and Romanians will arrive amid huge opposition to immigration. YouGov, a pollster, found in October that just 33% of Britons think the right of EU citizens to live and work in other member states a good thing.

This antipathy is partly due to the sheer numbers that have arrived since 2004—many more than the government predicted. Immigration has become entangled with a general mistrust of politicians, intensified by scandals over expense claims. The economic crisis has made everybody less tolerant. Without it, people would have been annoyed about immigration but got used to it, reckons Mr Denham.

The Poles’ experience is both good news and bad for Bulgarians and Romanians. It suggests that shifting public and political opinion will be hard, perhaps impossible. But, as Mr Denham was told by one of his constituents, “it’s not the migrants I don’t like, it’s the migration.” The experience of living in Britain, alongside its grumpy natives, may be happier than the rhetoric implies. It can hardly be worse.