Politicians in Britain are rarely positive about immigration these days. When Labour’s Yvette Cooper criticises the home secretary, Teresa May, her focus tends to be the Home Office’s legendary incompetence, rather than the merits of its immigration restrictions. But far from raising the drawbridge, Britain ought to open up more to diverse, dynamic and desperate newcomers.

It is shameful that Britain has admitted a mere 143 refugees from the civil war and Islamic State barbarism in Syria. It is outrageous that living with your spouse from outside the EU is now a privilege of the rich: those who earn less than £18,600 a year can no longer obtain a visa for the love of their life. It is absurd to deter international students, whose fees subsidise their local counterparts, whose spending supports local jobs, whose different perspectives enrich Britons’ university experience – and whom most voters don’t even consider immigrants. As for stopping people from coming here to work and contribute to society, it makes us all worse off.

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It is precisely because newcomers are different that they are so beneficial, since their differences tend to complement local needs and conditions. They may have skills that not enough Britons have, like medical training or fluency in Mandarin. They may have contacts that open opportunities for trade and investment as the centre of gravity of the global economy shifts east and south. They may be more willing to do gruelling jobs that most British people with higher living standards, education levels or aspirations spurn, like picking strawberries or caring for the elderly. They may simply be young and hard-working, a huge bonus for an ageing society with a shrinking local workforce and increasing numbers of pensioners to pay for. Having moved once, they tend to be more willing to move again, enabling the job market to cope better with change. And their diverse perspectives and experiences help provoke new ideas, while their dynamism tends to make them more entrepreneurial than most.

In advanced economies like Britain’s, sustained rises in living standards come from finding new and better ways of doing things and deploying them across the economy. Brilliant new ideas sometimes spring from individual geniuses – and those exceptional people are disproportionately migrants: three in ten of Britain’s Nobel laureates were born abroad, including Andre Geim, a Russian-born scientist who discovered a revolutionary super-material called graphene at the University of Manchester. But innovation mostly emerges from creative collisions between people – and two heads are only better than one if they think differently. A growing volume of research shows that groups with a diverse range of perspectives can solve problems – such as developing new medicines, designing computer games and providing original management advice – better and faster than like-minded experts.

Newcomers are also twice as likely as locals to start a business – just look at all the foreign entrepreneurs in Tech City – creating jobs, new products and services and wealth for the rest of society. Like starting a business, migration is a risky venture that requires hard work to make it pay off – and for newcomers who lack contacts or a conventional career, it is a natural way to get ahead.

Thus immigrants make the economy more dynamic – and far from putting unbearable pressure on jobs, public services and housing, they help improve the locals’ lot. Newcomers create jobs as well as filling them – when they spend their wages and in complementary lines of work. Polish builders create jobs for British architects, supervisors and suppliers of building materials. Overall, migrants tend to boost local wages, precisely because of those complementarities. Falling real wages in recent years are due to the crisis, not immigration.

Migrants also pay more in taxes than they take in benefits and services, as Christian Dustmann of University College London and others have shown. Educated abroad, migrants are typically young and healthy and more likely to be employed than locals. Those who leave again typically don’t claim a pension.

That migrants are net contributors to public finances is remarkable, since the government is spending much more than it raises in taxes and borrowing the difference. Indeed, newcomers’ taxes help service and repay debts run up by the existing population. Britain’s net public debt is around £20,000 per person. So if official projections are right and the population rises by 10% to 70 million in 2027, that increase would reduce the debt burden by £2,000 per person.

Since migrants’ taxes more than pay for the services they receive, any strains on public services are the government’s fault, not theirs. After all, if a British person moved from Liverpool to London and local services couldn’t cope, who would be blamed?

Nor is Britain “full up”. Even in England only 11% of the surface area is lived on. The problem is planning restrictions that excessively restrict development, driving up residential land prices to the benefit of large landowners and at the expense of everyone else.

A more diverse Britain would be great. Across the country, one in eight people were born abroad. In London, three in eight were. That diversity is something that most Londoners cherish, an essential part of the city’s identity, a magnet for talent and a magnifier of it. Of course, if some people aren’t comfortable with those whom they perceive as different, all the facts in the world may not persuade them that diversity is a good thing. But prejudice is not a sound basis for public policy.

• This article was amended on 26 March 2015. A statement that immigrants who leave again never claim a pension has been clarified to say that they typically don’t do so.