The Abolition of the Slave Trade Act became law on 25 March 1807 and took effect on 1 May, at which time no slave ships would be allowed to trade at British ports, and taking part in the slave trade would be considered a felony (it would eventually be classed as an act of piracy).
It was, however, a shallow success, since the banning of the slave trade did nothing for those already in the British Caribbean (an estimated half-million Africans) and elsewhere who were still under the shackle and yoke of British run slavery.
Whilst the US quickly followed suit and also banned the slave trade, they did little to enforce the ban. Britain, on the other hand, ultimately apportioned over one-third of the Royal Navy to enforce the law.
Full emancipation would not be achieved until 1838 - the Emancipation Act was passed by the British parliament on 1 August 1933, with British slaves achieving a limited freedom under a draconian 'apprenticeship' system the following year. A new campaign brought this to an end, and full freedom in 1838.