Calculations behind a claim by David Cameron that around 40% of EU migrants received benefits within four years of arriving in Britain involved "uncertainty and limitations", officials said.

The Department of Work and Pensions (DWP) said the statistic cited by the Prime Minister in defence of a push to curb the right to welfare payments for new arrivals for four years was based on a "one-off ad hoc analysis" of a variety of data sets.

It also used figures from 2012/13, it said, meaning the picture could have changed.

Detail of the analysis was published after the assertion - in a keynote speech setting out the terms of his renegotiation of the UK's relationship with Brussels - was questioned by experts.

Think-tank the Centre for European Reform said data from the official, publicly available Labour Force Survey "puts the figure at 21% in the first quarter of 2015".

In the speech, Mr Cameron said: "We now know that, at any one time, around 40% of all recent European Economic Area (EEA) migrants are supported by the UK benefits system with each family claiming on average around £6,000 a year of in work benefits alone and over 10,000 recently-arrived families claiming over £10,000 a year."

The Times had been told ahead of the speech that the figure was 43%.

In a briefing note on the calculations behind the claim - published eight hours after the speech - the DWP said it was able only to put the figure at somewhere between 37% and 45% "in order to reflect the uncertainty and limitations in the use of the data sets to produce this analysis".

It calculated that there were 95,000 to 105,000 claims from those arriving in the previous four years - and then allowed for those believed to have partners or children with them.

"This provides an estimate of between 195,000 and 235,000 EEA nationals who were in households in receipt of benefits or tax credits at March 2013 having arrived in the preceding four years," it concludes.

Around 66% involved a main claimant or their partner recorded as being in work and 34% out of work.

The note said: "The statistics in this report present a one-off ad hoc analysis in support of the Prime Minister's speech."

Setting out the list of different statistics brought together to come up with the figure, it went on: "There is no single data set that is readily available which allows the production of robust analysis on this topic from a single source."

"This data set provides the greatest capability to examine the topic covered in this ad hoc release."

The calculations "reflect a combination of the labour market conditions in the UK at that time, the individual benefit entitlement rules and migration patterns in the period to 2013.

"It is important to note that each of these is subject to change over time," it added.