611,779 "non-active" EU migrants were living in Britain last year, up from 431,687 just six years ago. The total is equivalent to the population of Glasgow;
The number of EU migrants coming to Britain without a job increased by 73 per cent in the three years to 2011;
The current annual cost to the NHS of "non-active" EU migrants is estimated at £1.5?billion (1.8 billion);
In contrast, the estimated cost to France's health system of "non-active" EU migrants is a fraction of that to the NHS, at just £3.4 million.
The report was written for Brussels and ordered by Laszlo Andor, the socialist commissioner in charge of employment and social inclusion.
The Sunday Telegraph can disclose that he is to bring a court case to make it easier for European migrants to claim benefits in Britain.
He will challenge a scheme that makes certain benefits available only to migrants from the EU who are "economically active" and is intended to make Britain less attractive to so-called benefit tourists.
But the EU-sponsored legal case would overturn this scheme, a move the Department for Work and Pensions said would make Britain more attractive to people wanting to live off the state.
Meanwhile, a court case last week detailed how a gang of Czech benefit fraudsters stood to make £1 million in bogus claims for child tax credits and child benefit, emphasising that benefit tourism can also include fraud on a vast scale.
Eurosceptic MPs said last night that the study and court case showed that Britain had to tighten up its borders and introduce stronger controls on welfare handouts.
The Government currently has no idea how much of Britain's welfare budget, including unemployment benefits, is given to EU citizens because a claimant's nationality is not recorded in the system.
Douglas Carswell, the Conservative backbench Euro-sceptic MP, said yesterday: "It is extraordinary how the European project has debased and debauched the original, noble idea of the welfare state.
"These figures show that the wave of benefit migrants has become a tsunami of economic refugees fleeing the eurozone crisis to try to find jobs here.
"We cannot both continue the free-at-the-point-of-use welfare state and benefits system and allow Europeans to flee the eurozone and come here.
"It is decision time. I would rather we quit Europe and had our own system of social protection."
The details of the report are the first concrete assessment of the impact of mass migration on Britain and other countries from predominantly eastern European countries including Poland, Lithuania, the Czech Republic and Slovakia.
The report studied the numbers of unemployed EU citizens coming to Britain looking for work, showing that the number coming without jobs has risen by 73 per cent in three years.
The report suggests that: "Between 2006 and 2012 there has been a steady increase of 42 per cent in the number of non-active EU migrants in the UK. While between 2005 and 2006 the growth of non-active EU migrants in the UK stagnated, since 2006 it has been steadily rising.
"A particularly high increase can be noticed between 2009 and 2011. The number of job-seeking EU migrants increased by 73 per cent between 2008 and 2011, while the total EU migrant population (active and non-active) increased by only 28 per cent."
The report also shows the extraordinary burden on the NHS, concluding it is equivalent to more than one per cent of the total NHS budget of £1.5 billion.
The NHS is under financial pressure because although it is excluded from government austerity measures, demands on it are outstripping the growth in its budget.
Only Italy, of the major countries, came close to such a burden on its health care system, with a bill of £620 million, the report finds.
Open Europe, the think tank, said evidence from the study described as a fact-finding analysis suggested Britain was counting the cost of an EU migrant boom.
The rise suggests that many EU citizens have been coming to Britain as a result of economic difficulties, especially in eastern Europe and Mediterranean countries such as Greece and Portugal.
Although the report details the cost to the Government in stark terms, it comes with a conclusion that there is "little evidence" that EU citizens came to Britain to collect state benefits and the practice known as "benefit tourism" was largely a myth.
The study states "the vast majority of migrants move to find (or take up) employment". The report concludes that "the budgetary impact" of claims by "non-active" EU migrants "on national welfare budgets is very low" and adds: "The same is true for costs associated with the take-up of health care by this group."
Open Europe said the report was misleading "possibly wilfully" in its conclusions and in apparently ignoring the evidence its authors had gathered.
Mr Andor, who commissioned the report, is to use the conclusions that migration is mostly for work as part of a landmark European Court case he is bringing against the Government.
Mr Andor has accused Britain of discriminating against EU citizens by restricting their ability to claim state benefits through a "right to reside" test introduced in 2004 to stem the flow of claimants from the new Eastern European member states. The test does not apply to UK citizens.
Mr Andor plans to lodge a legal action with the European Court of Justice. If successful, it would outlaw the "right to reside" test.
This would open Britain's benefits system to tens of thousands of extra EU citizens at an estimated cost of £150 million although the figure could be far higher.
Iain Duncan Smith, the Work and Pensions Secretary, has suggested the figure might be as high as £2 billion.
Experts point out that while most EU migrants may move between countries to look for jobs the British system makes it easier than most other countries' to claim benefits.
This is because British benefits are based on means-testing rather than on the recipient having made previous national insurance contributions.
European law says all EU citizens in a member country must have the same rights, so it is illegal to stop migrants from the rest of the EU claiming the same as British citizens. Similarly, NHS facilities are not dependent on paying any form of health insurance, as they are free at the point of access.
Conversely, the law means British people who move to countries such as France which only pay benefits to people who have contributed in the past cannot receive benefits and are likely to face severe restrictions on health care.
Stephen Booth, research director at Open Europe, said: "The European Commission is, wilfully or otherwise, presenting this whole issue misleadingly. It is the European Commission that is attempting to move the goalposts by taking the UK to court over the existing safeguards that ensure the UK's welfare system is not abused.
"If the commission gets its way, the UK's rules for gaining access to benefits will be relaxed substantially."
The Department for Work and Pensions said last night it would resist attempts by the EU to weaken its "right to reside" tests. A spokesman said a new, streamlined universal benefits system would make it more difficult to abuse.
The spokesman said: "We have strict rules in place to protect the integrity of the British benefits system and make sure it is not abused.
"We are also going further by strengthening the habitual residence test and time-limiting how long some migrants can claim benefits."
The commission has accused the Government of failing to provide proof of the extent or even existence of "benefits tourism".
A submission to the report's authors by the Government said it did not keep statistics on the nationalities of benefits claimants.