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Because the British Nationality Act gave Commonwealth citizens free entry into the United Kingdom in 1948. This coincided with post-war labour shortages. As a result, market demand recruited large numbers of migrant workers into Britain. It is this availability of jobs, not mere disparity in GDP, that attracts immigrants.
However, it's inaccurate to characterise the immigration as taking place at any particular "point" in time. British Indian and Black populations didn't suddenly explode right after 1948; the flow slowly increased over many years. As late as five years after the war had ended:
The non-white population began to grow but even in 1950 the total numbers in the whole of Britain were probably less than 50,000.
Thompson, Francis Michael Longstreth, ed. The Cambridge social history of Britain, 1750-1950. Cambridge University Press, 1992.
In fact, the biggest proportional increase in the British Indian population didn't happen until the 1960s when it more than quadrupled in a decade. A notable factor is the exodus of British Indians from Africa, who had migrated there during the days of the Empire. Faced with intimidation, discrimination, and in the case of Uganda, outright forced expulsion, many of them utilised their British passports and resettled in Britain.