It calculates that exports to the European single market are worth £211bn – or £3,500 per head of population – and particularly boost employment levels in less-prosperous parts of the UK.

In the light of the figures, hardline eurosceptics were accused of contemplating an “act of madness” by calling for Britain to pull out of the EU.

A previous estimate suggested that between 3 million and 3.5 million British jobs are linked to exports to the EU, the world’s largest trading group.

But the Centre for Economics and Business Research (Cebr) has concluded that the figure has climbed by around a quarter to 4.2 million jobs, or more than 13 per cent of the national workforce.

It comprises 3.1 million jobs directly supported by  sales to EU markets as well as another 1.1 million which are indirectly supported.

The new research is likely to be cited by Nick Clegg, the Deputy Prime Minister, when he goes head to head with the Ukip leader, Nigel Farage, on Wednesday in their second debate on the EU.

Sir Richard Ottaway, the Tory chairman of the Commons foreign affairs select committee, said of the findings: “I’m not surprised given nearly half of Britain’s trade is with the EU. The benefits of membership exceed the downsides.”

The research, commissioned by the British Influence group, also discovered that the boom areas of London and the South-east of England were the regions least dependent on EU trade for jobs.

Around 15 per cent of employment in the East and West Midlands and about 14 per cent in Yorkshire, the North West and Wales is linked to the EU, according to the Centre for Economics and Business Research (Cebr).

The figure falls to 11 per cent in the capital and 12 per cent in the South-east.

It also concluded that EU-related employment in white-collar jobs, including professional, technical and scientific services, has doubled since it last investigated the situation in 1997.

But the number of manufacturing jobs supported by EU exports has fallen in line with the UK-wide trend over  the period.

British Influence stressed that the jobs would not necessarily be lost if Britain quit the EU, but demonstrated the levels of employment “supported” by exports to the bloc. The Cebr acknowledged that demand for British exports had grown faster in emerging markets than in the EU.

But it added: “In terms of the absolute volume of goods, the numbers have steadily increased and the EU remains the UK’s single-biggest trading partner by a wide margin.”

Supporters of leaving the EU argue that such figures are a “myth” and that extra regulations from Brussels and the costs of membership are actually costing jobs.

Frances O’Grady: ‘One in seven British jobs already depend on trade with the rest of the EU, and these four million jobs tend to be more highly skilled and better paid than most’

But Frances O’Grady, the TUC’s general secretary, said: “One in seven British jobs already depend on trade with the rest of the EU, and these 4 million jobs tend to be more highly skilled and better paid than most.

“Jobs in the Midlands and Yorkshire are even more reliant on exports to Europe than jobs in other parts of the UK.

“The recovery won’t deliver for large parts of the country if the needs of the regions are ignored,” he said.

The former Conservative Foreign Secretary, Sir Malcolm Rifkind, said: “What is undoubtedly true is that there are a lot of jobs that come out of our being part of the  single market.”

He said that Britain could have access to the market outside the EU but at a heavy price, which would make it “pretty dumb” to leave  the union.

Peter Wilding, the director of British Influence, said that the research represented an “effective barometer reading of the jobs and wealth generated by that ongoing and vibrant trading relationship”.

He said: “It would be absurd to claim that all that would evaporate overnight if we were to withdraw from the EU.

“But it would surely be an act of madness to jeopardise economic reality based on facts in favour of little more than a pipe dream of alternative trading relationships articulated by those who propose that we should  walk away.”

Douglas McWilliams, the executive chairman of Cebr, said: “As the debate of the UK’s relationship with the EU continues, I think it is important that debate understands a sizeable chunk of the UK economy is supported by demand from EU member states.”