I'd disagree that they should pay, but just looking at the West Africa Squadron, which grew to be about 1/6 of the Royal Navy, at the time
the naval hyperpower, despite the fact that the casualty rate was five times higher (mostly due to disease) than the Home or Mediterranean Fleets, that's going to be fairly expensive.
Not to mention the fairly substantial bribes the UK paid to allied countries (Spain and Portugal) to stop the trade, and their technique of turning up at African capitals with fully fledged warships and suggesting to monarchs who were opposed to ending the slave trade that perhaps their successors would be.
One naval historian on youtube did a piece on them here: