Slaves were purchased and traded throughout Europe. Most of them were bought then sent to work on plantations overseas. It is not unlikely that many were also kept as household slaves and farmworkers in Europe. I guess some people didn't have the financial means to own slaves.
they weren't cheap. You still had to feed, clothe and house them if you wanted to get anything out of them, quite apart from the cost of buying them in the first place.
And also, some people thought slavery was wrong. In 1772, in a law case dealing with a man who brought a slave to England, it was argued that 'the air of England is too pure for any slave to breathe' and the slave was freed
Don't forget Wilberforce and the Slavery Abolition Act applied to the British Empire, not just the UK.
The Portugese and Spanish were big slave traders as well
To be successful in the African slave trade, it was necessary to have a good sailing fleet and good relations with African chiefs. The Spanish, Portugese and British were excellent at all these skills.
Only the very wealthy could afford to keep slaves within Europe, however. Most African slaves owned by Europeans worked on plantations within the British Empire and Spanish and Portuguese colonies.
Don't forget the Middle Eastern countries also had African slave labour.
Wilberforce's campaign was against the slave trade rather than slavery. When slavery was later abolished, it was throughout the empire, as Ethel says (particularly the sugar plantations of the West Indies). I don't think there were many slaves held in Britain itself.