She revealed in April that one in four people living in Boston, Lincs, were from eastern Europe – believed to be the highest proportion of immigrants in any town or city in the country.

Shadow immigration minister  Damian Green said last night that Mr Byrne was “floundering in the face of the evidence, denying the facts while still trying to sound tough.”

Mr Green said: “This cross-party committee, filled with senior Labour peers and experts, has made it clear that the basis of the Govern-ment’s arguments are wrong and that Labour’s weakness has let down the country.

“The committee even supported Conservative calls for a limit on immigration.”

And Sir Andrew Green, chairman of Migrationwatch UK, said: “This is an absurd attempt to counter-spin.

“This committee is one of the most authoritative in parliament.”

Mr Byrne, who attended yesterday’s Cabinet meeting, has already clearly signalled his view. In a speech last week he said the Lords’ Economic Affairs report was wrong.

And he added: “No matter which way you look at it, there is a good economic case for carefully controlled migration.”

A Downing Street spokesman said yesterday’s Cabinet meeting was “mainly on the potential benefits” immigration brought to the country and the economy, but “also relevant for ministers round the table was the impact on public services”.

The Lords’ report provided a point-by-point destruction of the supposed benefits of immigration to the UK.

It concluded there was no economic benefit and called on the Government to impose a limit, which ministers repeatedly ignore.

It said immigrants themselves were the “biggest winners” of current policy and dismissed claims that migrants were needed to fill jobs and support the growing demand for pensions.

It further warned that the in-flow could be forcing up unemployment among young Britons and pushing down wages.

The committee included two former Tory Chancellors, Lord Lawson and Lord Lamont, and leading economist Lord Layard.