Slave revolts are expensive, especially in the Caribbean, also Americans took over the slave trade
Others have given good reasons materially, but we shouldn't ignore that there really was a mass anti-slavery movement in Britain with an idealist base. and that those people do deserve praise.
People do decide what to do with the restrictied material options given them, and here they chose to abolish slavery, when other, more horrible, options for resolving this contradiction existed (See US Post-Reconstruction for instance, for how to somehow manage to do it worse than England's piecemeal, flawed, incomplete abolition of slavery.)
While this was not the sole reason, it should be noted that English anti-slavery laws gave their navy a pretext to board and search vessels for "inspections". With the UK quickly becoming the world's dominant naval power, this gave them lots of power over foreign shipping and trade, especially in the Atlantic.
"inspections"? why would UK ships want to have this excuse on hand?
It allowed them to intercept ships to check if they were slave trading. While they were inspecting the ship, the British officers could use the pretext to find other things wrong, ie smuggling, piracy, desertion, ect. Then they could seize your property or arrest you in some cases. Sort of like how American cops can use a busted taillight to pull you over, then arrest you if he find drugs during that.
The navy did also free a significant number of slaves this way too so it wasn't just an abuse of power, but it also signaled to everyone that Britain was the dominant naval power in Europe now.
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