AHC: African American immigration to Britain post WW2.

OTL, Post WW2, the UK invited immigrants from its colonies or former colonies, including predominantly black colonies like Jamaica, to fill up the labor shortage caused by WW2. Also, during WW2, many African American soldiers were pleasantly surprised by how well they were treated by British locals, in contrast to the Jim Crow racism they've endured their whole lives in the States. I'm wondering, were there ever any issue of blacks in the US trying to immigrate to the UK post-war? It would seem like many African Americans, having witnessed what they deem as some sort of racial utopia (obviously Britain has its racism problem, but was far less pronounced than Jim Crow ever was), and the British demand for more labor, would mean African Americans would be attracted to move to a country where they can find employment and escape Jim Crow. However, I never heard of African Americans being part of the mass immigration influx to the UK post war, it was mainly Jamaicans, South Asians and people from other parts of the British Empire. Was it ever possible to have African Americans be a part of the mass immigration wave to the UK post World War II, even though America was obviously not a part of the British Empire?
 
Black US incomes were far higher than Jamaican incomes at the time. Per the revised Maddison database, in 1955 the US's GDP per capita was $10,900 in 1990 dollars, the UK's was $7,800, and Jamaica's was $2,000. There was a large black-white wage gap in the US at the time - blacks made on the order of 40% less than whites - but the gap between the UK and black America wasn't enough to sway people to migrate across oceans.
 
Not really relevant to the thread, but an important reason why so many West Indians emigrated to Britain after World War II was that the US Government had made it harder for them to emigrate to the USA as they had done previously. Two prominent examples being the Jamaican parents of Colin Powell and Sidney Poitier born in Miami to Bahamian parents.
 
Had the British government been less racist that might have solved the problem of a certain number of white brit black US couples
 
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