The floodgates really opened after Blair took over in 1997. Any attempts at immigration control were deliberately abandoned as part of a new but unannounced gov’t policy. The idea was to force a “multi-culti” society on the country (and no doubt increase Labour party rolls) and enable any criticism of the policy to be deemed “racist” and thus discredited.
There were reports that it was indeed policy but proof only emerged years later in a leaked memo.