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The number of immigrants arriving in Britain from the European Union was undercounted by half a million over a ten year period, a difference the size of Manchester, campaigners have warned.

The mistake was discovered by the Office for National Statistics (ONS) in May when they compared the results of the 2011 census with the population that they had expected to find on the basis of births, deaths and official immigration figures, Migrationwatch UK said.

This discovery means that immigration between mid 1997 and mid 2010 now totals nearly four million, rather than the 3.4 million recorded.

And Migrationwatch UK has written to the UK Statistics Authority watchdog to insist the ONS revises the official immigration numbers for the period - something the group claims it has refused to do.

Migrationwatch UK chair Sir Andrew Green said: "Four million immigrants in 13 years is an astonishing figure - the highest in our history, including the Norman conquest in 1066. This new information underlines the scale of the task faced by the present government in getting the numbers down."

He added: "There is no point in burying bad news in obscure documents. That simply destroys trust. It is hard to think of set of statistics that is more important to the public.

"For the sake of public confidence in government statistics there must be a thorough revision of the immigration statistics and the new figures must be published without delay."

Migrationwatch UK added that allowing for the one million British citizens who emigrated in the period between 1997 and 2010, net immigration comes to three million.

The revelations comes as Britain prepares for access restrictions to its labour market to be lifted for Romanians and Bulgarians at the end of the year.

The UK Government has so far refused to provide official estimates as ministers believe they would not be reliable.

But campaigners such as Migrationwatch UK have warned that up to 250,000 Romanians and Bulgarians could arrive in the first five years after the restrictions are lifted on January 1 2014.

In a letter to UK Statistics Authority chairman Sir Andrew Dilnot, Sir Andrew said the "significance of the error underlines the scale of the task now facing the present government".

He added: "It is hard to think of a statistical series that is more sensitive in terms of public opinion, particularly at present."

A statement from the UK Statistics Authority said: "The UK Statistics Authority received a letter from Sir Andrew Green dated 8 July regarding long-term migration statistics. The authority is looking at the points raised and will respond publicly in due course."

Paul Vickers, head of population outputs at ONS, said: "It is simply not true to suggest that ONS has 'refused' to revise migration estimates.

"ONS produced a revised population estimates series which incorporates the net migration findings from the 2011 Census.

"The series, going back to 2002, was published in December 2012.

"At the same time we announced plans to publish a report analysing the quality of the long-term international migration data since 2001, including impacts of the improvements made to the data since this period. This will be published in the autumn."