Mr Blair's government--or even a Labour government led by some successor to Mr Blair--is unlikely to move far left because there is no plausible position far to the left to move to.
Such was their apparent understanding of human pathophysiology that they were usually able to offer plausible, immediate explanations of anything, make a rapid assessment, and move on.
The government's migration advisory committee says there is evidence Bulgarians would move to Britain because of its stronger economy, and it was "plausible" Romanians would come for the same reasons.