The UK government has consistently declined to provide evidence to support its claims about "benefit tourism", the European Commission has said.
Spokesman Jonathan Todd told the BBC the Commission had been asking for more than three years for the figures.
"One can but sincerely hope" for ministers to set the record straight, he said.
But No 10 said there was "widespread and understandable concern" over people coming to the UK to access benefits.
The Commission's intervention follows its publication of a report claiming that jobless EU migrants make up less than 5% of those claiming social benefits in most of the EU member states studied.
Some newspapers have noted that the report shows that there are more than 600,000 "non-active" EU migrants in the UK - describing them as "unemployed".
But the Commission said this figure included older schoolchildren, students, the spouses of migrant workers, and retired people.
Fewer than 38,000 were claiming Jobseeker's Allowance, it added.
"The vast majority of migrants go to the UK to work, and they actually contribute more to the welfare system than they take out, purely because they tend to be younger than the average population, and of working age," Mr Todd told the BBC Two's Daily Politics.
"The more EU migrants you have, the better off your welfare system is."
He said that if the UK government could show evidence of "systematic, widespread abuse of benefits by EU migrants", then the Commission would look at changing EU rules.
The spokesman argued that it was important to deal with facts rather than perceptions.
The report, carried out by a consultancy on behalf of the Commission, concluded: "The share of non-active intra-EU migrants is very small. They account for a similarly limited share of SNCB [special non-contributory cast benefits] recipients and the budgetary impact of such claims on national welfare budgets is very low.
"The same is true for costs associated with the take-up of healthcare by this group."
But Prime Minister David Cameron's official spokesman said: "There is an issue around access to the welfare system, around fairness as well as a cost issue."
"We don't think the current system is working, that is why we are looking at changes across the board," he said.
The government is currently conducting an audit of the cost to the NHS of "health tourism", he added.
Work and Pensions Secretary Iain Duncan Smith said there was a "big question mark" over the statistics.
"I am aware that this 600,000 figure doesn't actually refer to those who are necessarily of working age over here who could actually be working," he explained.
"I don't want to get in the middle of a debate between some of the media and the EU," he told MPs on Monday.
But he strongly criticised the Commission for mounting a legal challenge to the UK government's attempts to tighten the residency restrictions on who can claim UK benefits.
Conservative backbench MP Stewart Jackson told Daily Politics: "These people have not contributed.
"If you're a pensioner from Portugal or the Czech Republic you've not contributed. If you're a schoolchild, no-one would expect you to have contributed, but we're not in a parallel universe.
"Those children have got to be housed. They've got to have healthcare. Above all they've got to have school places.
"The strain in hot-spots, like my own constituency of Peterborough, is very, very acute, and I think that's why we're right to be saying there is an element of benefit tourism, particularly from the Czech Republic and Slovakia, and the government is absolutely right to be saying to the European Commission: 'Thus far and no further.'"