Short answer is no. These men had families and homes in America they wanted to get back to. Many of them went on to become prominent civil rights activists. Contrary to popular belief, the military was extremely racist. Many black veterans were so incensed by their treatment in the military during the war that they revitalized the civil rights struggle back home.

The long answer is they certainly weren't forgotten. Immediately after the war there arose the infamous "brown baby problem." Yes the British abhorred American Jim Crow but their attitudes were pretty hypocritical. Britain had its own racism problem rooted in imperialism. They may have disliked Jim Crow but not because they viewed people of color as equals. In Britain, as in America, it was illegal for white women to fraternize with black servicemen.

Well guess what, it happened anyways. WWII was a liberating experience for some women. Young women got to travel far away from the watchful eye of their familes. They experimented with their newfound freedom. Married women were estranged from their husbands for years at a time which gave them more freedom to do as they pleased.

After the war, many illegitmate mixed race children were being born in Britain. These children were known as "half-caste." They were looked down upon as inferior - their fathers were savages and their mothers were whores. The American government refused to provide relief for these children despite their willingness to compensate the British for virtually anything else (property damage, theft, etc.). The British government was also reluctant to do anything about the children. The question was whether these children could be considered British due to their racial morphology.

The Liverpool Association for the Welfare of Half-Caste Children declared that "mixed heritage" was " a handicap comparable to physical deformity." There were thousands of these children throughout southern England and Wales. They experienced harsh discrimination throughout their lives. Most were placed in children's homes and grew up in harsh conditions as nobody wanted to adopt a mixed race child.

Many of the mothers tried to file paternity suits but the US Army refused to cooperate. The opinion of the army was that black men were no more than beasts or slaves and were incapable of being fathers. They were only capable of siring offspring like animals. (Yes it was really this messed up, if anything I'm watering down the language used). Anyways, whenever a paternity suit was filed (they had to be submitted to the US Army) the Army responded that they had no record of anyone by that name thus foiling any attempts to establish paternity or contact with the father.

TLDR: Short answer no they went back to America. Long answer is they left a lot of bastard children in England.

Edit: I find it curious that this comment is receiving so much attention all of a sudden when it's been lingering in the dust bin for a month. Why?

Edit2: thanks to the two gentlemen who informed me of the meme. The sub auto deleted your comments before I could reply with a thank you. Kind of nice to see a bunch of people reading up on this forgotten history. The civil rights movement is so much more than what they teach in grade school.