Leading Tory Eurosceptics branded David Cameron’s renegotiation of British membership of the EU as a “farce” as they claimed the introduction of a new “national living wage” from next year would fatally undermine his plans to cut immigration.

In an escalation of hostilities over the in/out referendum, which could be held as early as June or July, the Vote Leave and Conservatives for Britain campaigns said that even if Cameron secured a four-year ban on EU migrants receiving in-work benefits, the higher “national living wage” announced by George Osborne in his July budget would act as a huge “pull factor” for migration that would render the reform all but irrelevant.

Steve Baker, the Tory MP for Wycombe and co-chair of Conservatives for Britain, which is expected to join forces with Vote Leave, said: “As the Office for Budget Responsibilty (OBR) has made clear, even if the prime minister secures a deal on migrant benefits, this wouldn’t have even the slightest impact on immigration flows.

“The living wage will make any tax credit cuts irrelevant, a fact the chancellor was relying on at home until recently. This whole farce makes clear that the renegotiation has become focused on a trivial issue that is fatally undermined by the facts on the ground. The only way to take back control is to Vote Leave.”

The intervention comes only two days after the prime minister appealed to fellow EU leaders to help address the concerns of the British people over immigration by backing his benefit reform plan. It is part of a concerted effort by anti-EU elements in his own party to paint the renegotiation as an exercise that will achieve little or nothing.

Other members of Conservatives for Britain include former Tory chancellor Lord Lawson, (the group’s president) former Tory defence secretary, Liam Fox (a vice-president), and Steve Bell, president of the Conservative National Convention, the powerful parliament of the voluntary party.

Cameron emerged from the Brussels summit on Friday encouraged by the response to his renegotiation plans from other EU leaders. But while he is likely to win agreement over plans to exclude the UK from the EU commitment to “ever closer union”, there is significant opposition to his other demands, particularly the plan for a four-year ban on EU migrants receiving in-work benefits, which other EU leaders say would be discriminatory against workers from their countries, and breach EU rules on free movement of labour.

Vote Leave, an umbrella organisation for Out campaigners, has compiled data which it says shows that even if Cameron were to achieve the four-year ban against all the odds, the effect would be, at best, minimal on limiting immigration. And if other EU leaders reject the plan, and fail to come up with an alternative, their figures suggest the “national living wage” would mean the UK would become far more attractive to workers from poorer EU countries, particularly those in eastern Europe.

According to its calculations a single Bulgarian worker is 377% better off working the same number of hours in the UK than at home. In 2020, when the living wage has been introduced in full, Vote Leave says the Bulgarian worker would be 353% better off even if they cannot claim in-work benefits, compared to 254% better off had the living wage not been introduced. Without the benefit reforms, the living wage will mean that a single Bulgarian worker is 483% better off, it says.

Asked if the “national living wage” – to be introduced at £7.20 for over 25s from next April, rising to more than £9 by 2020 – would act as a “pull factor”, the Treasury on Saturday restated its commitment to the policy. “Britain deserves a pay rise and the government is making sure it gets one – the independent OBR expects the “national living wage” to give a direct boost in wages for 2.7 million low wage workers.

“There are plenty of other countries in Europe which have a high minimum wage and the UK does not stand alone in that.”

Ministers say changes to the benefit system through the introduction of universal credit will also help discourage immigration.

But the arguments of Vote Leave are backed by independent academics and thinktanks. The Office for Budget Responsibility said the changes would make little difference.

Jonathan Portes, a senior fellow at the Economic and Social Research Council told the Observer that “the government’s new living wage for the over-25s may actually make the UK labour market more, rather than less, attractive to some EU migrants”.

He added: “If there’s one thing that both the ‘remain’ and ‘leave’ sides of the referendum argument can agree on, it’s that the government’s renegotiation proposals on migrant benefits are largely irrelevant. Both sides argue, rightly, that there are some very important issues, economic and political, at stake in this referendum. This isn’t one of them. No serious analyst – including those in Whitehall – think changes to benefit rules will have more than a marginal impact on migration flows.”