Well, the point of a rebellion against the state is generally to establish (or re-establish) the state. If the rebels are called British rebels, then they'll be trying to change Britain's government, and not establish a country of their own.

That said, if a peace settlement could be achieved, after hacking of the save game (if it's possible and if it's easy enough for the average player to do it), you could change the name of that rebel faction (maybe change a couple of other things like strategic map colour and the banner of the faction), you could have your very own emerging faction under your control!

But I'm getting ahead of myself here. We'll just have to wait and see (and hope a dev posts here!)