The contribution of immigrants to the British economy is very slight indeed and the main benefits are to the migrants themselves
Migrationwatch UK says the economic benefit is equal to 4p a week for each person in Britain.
Its chairman Sir Andrew Green accused Whitehall of trying to divert attention from the problems caused by migration.
A Home Office spokesman said there was "a clear consensus" that migrants had helped the economy to grow.
But Migrationwatch said its figures showed immigration's benefit to the UK was far lower than claimed.
"What we have done is to look at the economic contribution of migrants, taken as a whole, taking the economy as a whole," Sir Andrew told BBC News.
"We find they certainly do add to production, but they also add in virtually the same proportion to population."
The benefit of mass migration to each individual member of society was "trivial", Sir Andrew added.
He said the main beneficiaries were the immigrants themselves, who were able to send home about £10m each day.
Migrationwatch reached its conclusion by comparing the proportion of the population who arrived as immigrants in 2005 with Treasury estimates for the proportion of GDP growth coming from immigration.
The difference between these figures, it said, amounted to a 4p gain for each person in the UK per week - or about £2.10 a year.
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