Wilberforce
BACKGROUND:
All kudos to Wilberforce, a man deserving much esteem. As a member of Parliament [Great Britain (GB)] he 'owned' a "Rotten Borough" seat that was his as long as he paid for it out of his considerable fortune. As such, he was well able to enjoy the 'good life' with minimal responsibilities BUT he CHOSE to take bigger issues like the slave trade.
For GB there are 2 dates concerning control of slavery via Parliamentary Acts (laws). The first was the ending of the English transportation of slaves, as property, from Africa to elsewhere, "Foreign Slave Trade Bill". This was Wilberforce's big triumph in 1806-7 and it was very big because of the sugar plantations in the Caribbean Islands. These plantations were very lucrative in profits and taxes BUT almost totally 'farmed' by slaves. Cutting off the source of this labor pool meant a visible stumble at a time when England was fighting a death struggle with Napoleon & France. If you want to see how this war effected domestic England, look at the books and media like Poldark. Smuggling was a big issue because the Government levied HIGH Tariffs on common goods for that effort, think of 100-500% duties. Thus, stopping or reducing slavery to the sugar plantations could mean a necessary increase in those more local taxes.
Actions: GB & US
In the USofA, the 1st National move towards curtailing slavery is found in the 1789 US Constitution under Article 1, Section 9, Paragraph 1; "The Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a Tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person." This preceded Wilberforce by about 15 years in enacting a law.
For the Constitution Writers, they had the advantage of postponing enactment by the 20 years and the opponents that would otherwise be resisting were more worried about the chaos that would otherwise results under the Articles of Confederation. Additionally, it seems likely, that the slave proprietors thought that there would be other avenues for new slaves through the western frontiers, especially Spanish Mexico. In GB, the 1807-8 passage did not ban slave ownership, it just banned the transportation by GB merchant ships. It took till 1833 for another law for the abolishment of slave ownership. In the US, it took our Civil War of 1861-65 for that.
On the topic of Wilberforce's efforts towards the 1806-8 Parliament act, I commend the excellent movie "Amazing Grace" (2006) for a near hagiography of Wilberforce and his cohorts.