While trading slaves was abolished in Great Britain in 1807 it was not until 1833 that slavery was abolished. But even then slaves were not released from their bondage. They were to remain in bondage for periods ranging between six and twelve years after slavery had been abolished, though all were finally released just five years later in 1838. The British government paid slave owners around 20 million pounds in compensation for releasing their slaves which was a staggering amount that amounted to 40% of its annual revenue and incurred a debt that was not paid off until 2015 in doing so.
Scottish slaves gained their freedom much earlier thanks to Joseph Knight. In 1777 he challenged his owner in Court citing an earlier court decision which stated that a state of slavery was not recognized in Scotland. Ironically while Knight vs Wedderburn effectively freed all black slaves in Scotland, many coal miners were kept in a state of slavery until 1789.
I am unable to directly answer how freed slaves were treated in Britain after they were released, but I can provide some observations from my readings about British Columbia.
Sir James Douglas was the son of a Scottish merchant and a Creole mother in Guyana back in 1803. He was schooled in Scotland then signed on with the fur traders of the Northwest Company and shipped off to North America. He was placed in charge of his first post in 1828 and had reached the highest position of Chief Trader by 1839. He was instructed to create a new trading post on Vancouver Island in 1842 and was placed in charge of all of the fur trade along the British Columbian coast. When Vancouver Island became a colony Douglas became it's 2nd governor and later founded and became the governor of what is now British Columbia. In 1864 he was knighted by Queen Victoria.
In 1858, looking to bring new immigrants to his fledgling colony, Douglas invited the free blacks living in San Francisco to move up North. After swearing an oath of allegiance to the British Crown, these new immigrants were able to buy land and establish themselves like all other British citizens. Just over 300 accepted this offer and moved north. They joined the city police force, became carpenters, teachers, doctors, traders and even became elected as a Member of the Provincial Legislative Assembly.
In 1859, the citizens of Victoria heard of a young slave from Oregon territory that was being mistreated by his master. Knowing that the colony of Vancouver Island was part of the British Empire and that all slaves were declared free once they set foot on British soil the townspeople set out to free him. They sent a ship south to kidnap the boy and bring him back to Victoria where he was declared a free man.
Canadian fur traders in the early 1800's often married native women and fathered children with them. Dr John McLaughlin, the Father of Oregon, was one who had a native wife and family. His son, John McLoughlin Jr, was born in 1812. When he came of age, he was first sent to Upper Canada, now Ontario, to begin his schooling. From there he went to England and later France to study medicine.
In the Northern part of British Columbia where I live there is a portage, river and region named after a trapper named John Giscome. I have seen his name mentioned many times while reading the history of my area over the past 20 years, and it was only two years ago that I learned that he was one of the black immigrants from San Francisco. That all of his contemporaries mention him by name and don't mention his race would seem to indicate his acceptance by his peers.
So while it appears that racial segregation was not an issue in England there is another factor that existed. This was the division of people according to their class or station in life.
British citizens could rise up from humble origins to positions of peerage or knighthood. Sir James Douglas was one. Sir Alexander Mackenzie was knighted after becoming the first person to cross North America in 1792. But another explorerer, one who did more to explore the Arctic regions than any other person was snubbed by the establishment and denied recognition by his peers.
John Rae was an employee of the Hudson's Bay Company. When Franklin's expedition disappeared Rae was given the task to go search for him. During his search John Rae covered 1300 miles of barren Arctic lands on snowshoes and ultimately discovered the fate of Franklin's men. But because he embraced the native methods of travel and survival and dared to report back that Franklin's men resorted to cannibalism in their final days he ended up being ostracized by the collective establishment. Though he mapped 725 miles of Arctic shores and provided the routes used by future captains to sail the polar waters, credit was given to the British Navy's Captains instead. One member of the British Royal Geographical Society, in conversation about John Rae said "Of course anybody can succeed if he is willing to go native. The prime objective of foxhunting is not the killing of the fox, but the observance of good form during the pursuit and at the kill. The objective of polar exploration is to explore properly and not to evade the hazards of the game through the vulgar subterfuge of going native." Rae had been recommended for knighthood to recognize his Arctic explorations, but this was opposed by the Admiralty and members of the Royal Geographical Society as Rae was considered to be too vulgar for this title.
While I did not directly answer your question about how freed slaves were treated in Britain after slavery was abolished, I hope I have given you an indication of how life in general might have been experienced by them during this time.