Populist promises made in opposition have a habit of becoming the stubborn problems of government. This is especially true for coalition governments, and the Conservative Party is finding out the hard way, having made an ill-conceived campaign pledge to limit the number of non-EU migrants entering Britain to work.

In her Commons statement yesterday, the Home Secretary, Theresa May, announced a cap of 21,700 on the number of skilled workers from outside the EU. It included an exemption for "exceptional talent", for those earning £24,000 but staying for less than a year, and for those posted to Britain by their overseas employers – provided they earn £40,000 and stay for longer than a year. The figure is tighter than the 43,700 recommended by the independent Migration Advisory Committee.

The cap was intended to help bring annual net migration down "from the hundreds of thousands to the tens of thousands". But the ambition articulated by David Cameron before the election cannot be achieved by placing an arbitrary ceiling on a small proportion of new arrivals. Non-EU migration accounts for only 12 per cent of the total. Moreover, business leaders argue that any cap will damage Britain's economy.

Of non-EU arrivals to Britain, roughly a fifth are joining relatives, a fifth are skilled workers, and the remainder are students. Blocking close family reunions is immoral and may, in many instances, be illegal. Blocking skilled workers is bad economics. As for students, the ban on unskilled non-EU workers effective from 2008 did lead to a rise in student arrivals and, with it, abuses. These should be halted. But stopping other lucrative additions to a sector worth nearly £40bn to our economy is more than faulty economics: it risks damaging the international standing of British universities.

The exemptions reflect co-operation within the Coalition and represent a significant victory for Vince Cable, the Business Secretary. Ms May, who was the first to call Conservatives "the nasty party", had been expected to outline her measures with a rather nasty speech; but Mr Cable and Nick Clegg intervened, demanding that some of the restrictions be eased.

Business leaders have lobbied the Government for weeks, arguing they cannot generate a private sector recovery if they are hindered from hiring skilled foreigners. Yet, though they will take some satisfaction from yesterday's announcement, and though Liberal Democrats will present it as a pragmatic compromise born of economic necessity, there is a danger that the broader lesson of this episode is lost.

This is the first time that a British government has set a policy objective for net migration. That will please the hawks. But the cap announced yesterday does not deliver what David Cameron suggested that it would do. The brunt of the visa reductions, as Ms May made clear yesterday, will be borne by non-EU students. Mr Cameron will plead that his retreat has been forced on him by the reality of Coalition government; but it was dishonourable of the Conservatives to make a promise which they must have known could never be delivered.

As it is, the ceiling announced yesterday is not as bad as it might have been. But it will be costly, and it risks stoking resentment. Yes, immigration can cause social strains but the solution is to transfer funds to deprived areas and improve the skills of the indigenous workforce, not to criminalise the aspirations of foreigners who want to work here. Once elected, ministers would do better to admit the errors of opposition than perpetuate them in office. Any policy that is both ineffective and self-defeating is not worth pursuing. The immigration cap should be scrapped.