The Prime Minister David Cameron’s case for Britain remaining in the European Union (EU) has received a blow, as analysis of immigration figures has revealed that his much-vaunted ‘emergency brake’ on in work benefits will have almost no impact on net immigration figures.

The emergency brake is one of the central pillars of the Prime Minister’s renegotiation of Britain’s relationship with the EU, and has been cited by Mr Cameron numerous times over the last few days as he set out his arguments for Britain staying within the European bloc. He insists that the brake, which will reduce migrants’ access to in-work benefits for seven years, will drive down European immigration into Britain, addressing one of the key concerns of those wanting to leave the EU.

But analysis of British migration figures by think tank Migration Watch UK has revealed that the measure is unlikely to have any significant impact on the number of Europeans heading to the UK, as the vast majority are not entitled to in-work benefits.

Net migration to the UK is currently at a record 330,000 a year, of which just over half, 180,000, is from within the EU. But according to the report “half of new arrivals from the EU are single and a further quarter are couples without children. Neither of these categories are currently entitled to any significant benefits.”

And of the remaining quarter who do receive in-work benefits, upcoming changes to the way in which benefits are paid will see their entitlement tail off over the next few years anyway, further diminishing the impact of the so-called emergency brake.

Migration Watch found that just one demographic – single parents with dependent children – would be materially affected by the change, stating: “Restricting in-work benefits paid to these families could make them considerably worse off than at present, and the UK would not be an attractive destination for such families.” But it added: “However, single parents comprise less than 1 in 20 of families from Eastern Europe who first arrived in 2011.

Some of the single parents would have initially arrived without children, the researchers said, concluding that the more likely impact of restricting benefits to these people would simply be to discourage eastern European migrants from becoming single parents while working in Britain.

Yet the picture is even gloomier for this Conservative government, as not only does the report conclude the brake would have little effect, researchers also pointed out that the Chancellor George Osborne has announced plans to increase the national minimum wage significantly over the next few years. That, they say, will offset any reduction in income derived from cutting benefits.

The report notes: “A typical single person working thirty five hours on the National Minimum Wage (NMW) is currently entitled to about £2,000 a year in tax credits and housing benefit. However, in 2020/21 when Universal Credit will have fully replaced these benefits, the same person – by then working for the National Living Wage (NLW) – will receive nothing.

“However, he or she will still be better off in cash terms than currently as the boost to earnings given by the National Living Wage will be greater than the loss of in-work benefits.

“Half of the family units headed by Eastern Europeans who first arrived in the UK 2011 onwards fall into this category.”

Yesterday Mr Cameron side-stepped a challenge on this very question in the House of Commons from a fellow Conservative MP who asked “how much the welfare changes will reduce immigration from the EU in the coming year?”,

Mr Cameron replied: “Anyone who knows that, at the moment, someone can come from the EU and get up to £10,000 of in-work welfare benefits in the first year knows that that is a big incentive to come to Britain.

“Many people said that we would never be able to get changes to in-work benefits, but we have got those changes. If we pass this legislation we will see, in 2017, a seven-year period up to 2024 in which we will be restricting these welfare claims. That, plus all the changes that the Home Secretary helped to secure—in many cases reversing ECJ judgments—will actually restore to our country powers over welfare and powers over immigration that can make a real difference.”

But the Migration Watch report does not support this conclusion. Instead, it continues: “It follows that a single person, for example from Eastern Europe, would not be affected by any proposals to restrict benefits even for a four year period, once Universal Credit and the National Living Wage are introduced as planned.

“In practice, it is very likely that the availability of work in the UK is the main draw at present and that this incentive may be considerably increased by the higher wage differential between the UK and some other Member States likely to result from the National Living Wage.”

Commenting, the Chairman of Migration Watch UK Lord Green of Deddington said: “This outcome will make virtually no difference to immigration, nearly half of which now comes from the EU.

“Singles and couples without children have only marginal entitlements to benefits and most EU migrant families do not qualify for much in the way of benefits in their early years in the UK. The availability of work and salaries considerably higher than those at home are likely to be the main attraction.”