David Cameron's Government has claimed it has no information on how much EU migrants cost - or benefit - the UK.
Treasury Minister Lord O'Neill made the startling admission in a written Parliamentary answer that was quietly published while the Prime Minister was in Brussels.
Labour peer Lord Beecham asked the minister to reveal 'the annual benefits paid to EU migrants in the UK and the contribution of those individuals to the public purse through income tax receipts and VAT'.
Lord O'Neill replied with a five word answer: "The information is not available."
Lord O'Neill, who was appointed to the Government last year after the Tory election victory, is a former economist with Goldman Sachs merchant bank and usually has detailed figures at his fingertips.
But Government departments have been unusually coy about weighing up the cost despite months of questioning over claims that Britain's welfare system is a "pull factor" for migrants.
Shadow Justice Minister Lord Beecham pointed out that Mr Cameron was making migrant benefits a centrepiece of his Brussels renegotiation.
"It is extraordinary that the government, which is making such an issue about the impact of migrants on the nation's finances should turn out to have no information about what it is actually paying out in benefits on the one hand and receiving by way of taxes and VAT on the other," he told HuffPost UK.
"If Ministers continue to consider this a serious problem, they need urgently to commission a proper study of the actual situation and then publish the findings."
Eurosceptics will claim that the lack of transparency is because the cost is higher than thought, but pro-EU campaigners may counter that the Government doesn't want to admit that migrants put in more in taxes than than take out of the UK.
Downing Street claims that the issue is not just a matter of how much is spent on benefits but a sense of 'fairness' to UK workers who have spent years contributing to the welfare state.
Many migrants don't claim a penny in benefits, but the Government has repeatedly talked of the need to tackle "benefit tourism" to the UK.
Mr Cameron declared at the start of his EU renegotiation that "we can reduce the flow of people from within the EU by reducing the draw that our welfare system can exert across Europe".
Yet when asked to quantify just how much of a burden they place on the system, ministers have often been opaque.
Department for Work and Pensions statistics show that out of the 5 million people who claim welfare benefits in the UK, 114,000 (2.2 percent of the total) were EU nationals.
The most recent Freedom of Information request found that 84,000 EU migrant families claimed tax credits in 2013-14 and had been issued a national insurance number in the previous four years.
The main figure Downing Street tends to use to prove 'benefit tourism' is that "around 40 percent of all recent European Economic Area migrants are supported by the UK benefits system".
But economists claim the figure, based on an ad hoc DWP statistics release, is misleading and the UK Statistics Authority complained that its release was 'unsatisfactory'.
Some estimates suggest that one big source of migrant 'benefit' is housing benefit, paid out to low-paid EU nationals who often live in private rented housing.
On the vexed issue of British child benefit paid out to EU migrants who leave their children in their home countries, the most recent figures suggest that £27m is paid out every year.
There were 34,000 claims of UK child benefit for children residing overseas in EU states.
Government statistics show that recently arrived Eastern European migrants are actually unlikely to claim benefits - the vast majority of claimants have been here four years or more.
Jonathan Portes, former chief economist at the DWP and a senior fellow at the 'UK in a Changing Europe' think tank, said the UK Government now appeared to be concealing information.
"In the PM's recent speech he claimed migrants from the European Union were a significant burden on the UK benefit system. On closer inspection his statistics proved to be highly misleading at best," he told HuffPost UK.
"Now the Treasury is saying it can't provide any information at all on the tax contributions or benefit payments of EU migrants. That is not remotely credible.
"Again the government is concealing important information and data from the British people; whichever side of the referendum debate you are on, this should be unacceptable."
Michael O'Connor, a policy consultant for 'Stronger In Numbers', told HuffPost: "Whatever sums are actually being spent on in-work benefits for workers from other Member States, restrictions on payments to new arrivals - particularly if tapered - seem likely to make only very modest cost savings bearing in mind the low rates of claim in the early years after arrival in the UK.
"Any impact on levels of migration would be correspondingly low."
Despite headlines this week about 'EU migrants grabbing British jobs', some economists claim our booming economy is the real "pull factor".
And the UK's healthy growth has benefited Britons as much as EU migrants in the jobs market. Since Mr Cameron entered office, one million more Britons are in work and 850,000 more Europeans are working in Britain.
The number of EU nationals working in the UK passed the two million mark this week, but some analysts say that overall they contribute £2bn a year in taxes.
One study found that those from the European Economic Area (EEA - the EU plus Norway, Iceland and Liechtenstein) had made a particularly positive contribution in the decade up to 2011 - contributing 34% more in taxes than they received in benefits.