Interesting question: although the likelihood of this happening without a substantial POD beforehand is honestly rather low-particularly as the OTL ruling only applied to England and Wales(though, as per Wiki, Scotland banned it soon after in a separate case, in all three cases, it's lack of justification in common law was cited as a reason.)-but for the sake of this scenario, let's say an empire wide ban actually does happen.
It would be significantly more controversial than it was in 1837 IOTL when a genuine majority, particularly amongst the middle classes, generally supported abolition in Britain itself; 65 years earlier, abolitionism, while it did have it's supporters back then, was not yet a truly major force on either side of the Atlantic, not even in Britain itself.
What happens in the Colonies? Well.....this is honestly quite debatable. It could go any number of ways, but a couple that strike me as interesting eventual possibilities are, either the southern colonies break off and try to go off on their own(though this seems a bit unlikely), or it may mollify existing abolitionist elements up North enough to the point where they may be more hesitant to break away(which could lead to London making some significant concessions to the Northern colonies later on), or perhaps even both.
But again.....none of this is likely without a major POD.
As for the latter option, though,.....that probably doesn't change very much from OTL.