The abolition movement was genuinely popular, alongside a developing legal and religious situation that bestowed 'personhood' (to use a clumsy term) on people that were foreign or otherwise not British (who could not be slaves, by longstanding precedent). Religion had a lot of weight in social and cultural terms, and added to that, you had many respectable establishment people who took up the cause where Quakers and freed slaves could not; there was a genuine confluence of humanist and religious thought around slavery, which was not just in Britain. The French constitutions late in the 18th century also abolished slavery (although they were interrupted for other reasons), and events like the Haitian Revolution signaled a severe change in what people feared or predicted would come from slave populations. One of the political parties in the British Parliament, the Whigs, were ostensibly abolitionist, and only grew to be more so as time went on; this was a fairly obvious pressure point to use when the sugar trade grew to be less profitable, and slavery grew to be even more unpopular.

Certainly it wasn't entirely a moral issue, but it offered a sense of moral superiority and the economic case for slavery seemed to be getting shakier, alongside a much wider dissemination of just how inhuman the slave trade was, in terms of conditions, punishments, and deaths.