You might get an answer if you explain your question better.

If you mean "When did slavery start in the United Kingdom" it didn't. The United Kingdom has only existed from 1801, and slavery had already been banned in England and Scotland.

If you mean "When did slavery start in what is now the United Kingdom", then you may need to crosspost to r/anthropology. Slavery in Britain pre-dates the arrival of the Romans and thus written history; Roman sources talk of Gaulish merchants regularly buying slaves from British tribes pre-invasion. I'm not an anthropologist or archaeologist so I can't really say more on how it started.

Or do you mean "How did the Kingdoms of England and Scotland get involved in the African slave trade?" in the Early Modern Period?