I managed to find the news story from 2009 which mentions the role played by the Performance and Innovation Unit in there being a secretive Blair government policy to encourage much higher levels of immigration into the UK.
"The huge increases in migrants over the last decade were partly due to a politically motivated attempt by ministers to radically change the country and "rub the Right's nose in diversity", according to Andrew Neather, a former adviser to Tony Blair, Jack Straw and David Blunkett."
Mandleson admitted as much in a DT article (http://www.telegraph.co.uk/news/uknews/immigration/10055613/Labour-sent-out-search-parties-for-immigrants-Lord-Mandelson-admits.html May 2013)
".....his party got “the numbers wrong”."
There was a BBC Radio 4 program which covered the question of numbers. They (those advisers adn even the civil service) apparently made an "estimate" but didn't have anything solid upon which to make a reliable prediction.
They gave a maximum and minimum value to Labour who chose to use the lower value as the reported expectation but in the end the report was proven hopelessly wrong and had under-estimated the numbers by a very significant factor.
Of course, as the article then says (referring to Labour leader):
"But the party leader stopped short of admitting that immigration was too high. "
What I think they were really looking for were a new source of Labour voters.
Of course, immigration and the dilution of national identity is a key objective of the EU also and one suspects similar disregard of indigenous populations in the EU but also, a large enough influx of "citizens" likely to support the EU as being "better" than they were used to is probably why they have sought to admit as much of the old East block as possible and Turkey of course.