Just look at the difference in the historical treatment between blacks in Canada vs treatment of blacks in America. The treatment of blacks is very much an American issue.
Historically the situation could not have gone much worse for black Americans. The question of slavery became a question of cultural identity for the south as it entwined in with their desires for autonomy. Slavery became the sacred flag through which southern states could raise to their own independence, the very extent that they would ultimately go to war over the matter. Black Americans ultimately became the tragic casualty of these fractions between the embryonic American states and their struggle for unity.
Firstly to dispel the ever going myth that Tory government never implemented changes during the early part of the 19th century- look at Catholic emancipation or the 1844 Factory Act. William Pitt the Younger was a great proponent of parliamentry reforms. Look throughout 19th century British history and you'll quickly realise Tory and Conservative governments were the governments that actually enacted tangible, meaningful reforms (instead of making wild promises and delivering little).
Also what is this nonsense about Lancashire mills putting pressure on a southern anti-slavery movement? Roberts Loom was only patented in 1830. Slavery was outright abolished 1833. The textile revolution only truly got moving in the middle of the 19th century, long after any slavery question was being debated in the Commons.
1807 Slave Trade Act: 283 Votes for abolition, 16 Against Abolition. Note pre 1832 Great Reform Act)
If America had still been in the picture I don't think it would have shifted the picture all that much bearing in mind the West Indies still had a huge demand for cheap labour for the sugar plantations and yet the act was still comprehensively enforced. The compensation for slave owners would have simply been smaller than it historically was in 1833 on a pro rata level.