If I may be allowed to pick at that nit, which I personally find very annoying: we normally use "civilisation" to mean something bigger than an empire, or state, for instance "The Greek civilisation" but the "Macedonian Empire". Accordingly, the civilisation to which the British Empire belonged was the Western Civilisation (of which we are still a part).

And so, although the western civilisation led the movement to abolish slavery in modern times, the British Empire was not the first to do that. Other colonial powers came first- for instance, the French and the Spanish, etc.

Note that even on a civilisational level, slavery had been abolished before in various places, for instance by the Qin Dynasty in today's China, etc. Those were generally short lived but to be fair, it took a long time before the majority of the world stopped keeping slaves anyway, and abolition advanced with fits and starts.

And, unfortunately, some are still at it to this day, although not legally so.