The allegation was made after a former Labour adviser said the Government opened up UK borders partly to humiliate Right-wing opponents of immigration.
Andrew Neather, who worked for Mr Straw when he was Home Secretary, and as a speech writer for Mr Blair, claimed a secret Government report in 2000 called for mass immigration to change Britain's cultural make-up forever.
Jack Straw and Tony Blair 'covered up plan to let more immigrants in for political reasons'
It also emerged that:
Home Office Minister Barbara Roche, who pioneered the open-door policy, wanted to restore her Labour reputation after being attacked by Left-wingers for condemning begging by immigrants as 'vile'.
Civil servant Jonathan Portes, who wrote the immigration report, was a speechwriter for Gordon Brown and is now a senior aide to Cabinet Secretary Sir Gus O'Donnell.
Labour chiefs decided to brand Tory leaders William Hague and Michael Howard as racists to deter them from criticising the covert initiative.
Mr Neather said there was a 'driving political purpose' behind Labour's decision to allow in hundreds of thousands of migrants to plug gaps in the labour market.
He said the stance was foreshadowed by a report by Mr Blair's Performance and Innovation Unit (PIU) think-tank, which said the nation would benefit from more migrants.
Mr Neather claimed that earlier, unpublished versions of the report made clear that one aim was to make Britain more multi-cultural for political reasons.
'I remember coming away from some discussions with the clear sense that the policy was intended - even if this wasn't its main purpose - to rub the Right's nose in diversity and render their arguments out of date,' he said.
The report, entitled Research, Development And Statistics Occasional Paper No67 - Migration: An Economic And Social Analysis, was published in January 2001 by the Home Office, then run by Mr Straw.
Most of its key statistics came from a PIU team led by Mr Portes. The report paints a rosy picture of mass immigration, stating: 'There is little evidence that native workers are harmed by migration. The broader fiscal impact is likely to be positive because a greater proportion of migrants are of working age and migrants have higher average wages than natives.'
It goes on: 'Most British regard immigration as having a positive effect on British culture.'
Mr Portes remains an enthusiastic advocate of the benefits of immigration. He wrote a report for the Department of Work and Pensions last year rejecting claims that Eastern European workers had stolen the jobs of British counterparts, arguing Britons lacked the skills and motivation.
A former Government adviser told The Mail on Sunday: 'If the Government had been prepared to have an open debate about immigration, we would not have had the problems we have seen with the BNP. But it did not want immigration policy discussed.
'It is not a very honest Government. They knew immigration was a hot issue and they did not want to get into a fight on it.'
The source said Labour deliberately targeted William Hague and Michael Howard when they called for tougher immigration controls.
Mr Hague was accused of 'playing the race card' in 2001 when he said Mr Blair was turning Britain into a 'foreign land'. Michael Howard was called a 'racist' in 2004 after he went to BNP stronghold Burnley, in Lancashire, to denounce Labour's stance on asylum seekers.
A Labour insider suggested Mrs Roche relaxed immigration controls partly in response to the outcry she faced after criticising begging Romanian mothers.
'She was called a scumbag,' said the source. 'She wanted to show she was a genuine liberal.'
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