The sort of things that caused the Americans to rebel—being denied representation in Parliament, being denied the opportunity to expand at the Native Americans' expense (the Proclamation Line), being the victim of British mercantilist policies (the Tea Party)—didn't happen in Great Britain. The British, of course, did have representation in the Parliament of Great Britain; the Native American situation doesn't apply; and the mercantilist policies were tailor-made to benefit British interests.
It's noteworthy that one of the phrases used by Americans in the era leading up to the American Revolution was "rights as Englishmen" that they felt were being denied to them: that is, they felt that the British had traditional rights that the Americans ought to have but weren't permitted to have (due to George III taking direct control over the American aristocracy).
Things were far from perfect, of course, but the situation in Great Britain (with a democratically elected government, albeit with poor levels of suffrage and plenty of corruption) was very different to the kind of situation in the Kingdom of France. When presented with some degree of democracy, I think the first instinct is usually to work with it rather than to immediately seek out conflict, whereas in Bourbon France there was essentially nothing to work with and it was clear that any concessions were coming against the firm opposition of the established order; and even Revolutionary France remained a constitutional monarchy for quite some time before Louis XVI continued trying to roll back the Revolution and eventually they got rid of him. And there's no way George III or any other British monarch in this era would go repressive on what Britons considered their rights; the present British royal family is in power as a direct result of the then-very-recent Glorious Revolution (in 1688-1689), where a British king (James II of the House of Stuart, strictly speaking King of England and Scotland separately) had tried to make himself rather than Parliament the supreme force of the state and, as a result, his royal line, even though it had been governing Great Britain since the century-old personal union that had essentially made British unification a concept by putting England and Scotland together under one monarchy, had been deposed by force.
The interesting thing is that it wasn't the monarchy that was initially seen as oppressing the Americans, it was the Parliament of Great Britain, which was taking upon itself rights of governance that had previously been held by the monarchy and devolved to American colonial assemblies. When King George III proclaimed the Patriots (many of whom were claiming to be loyal to the King and merely enemies of some of his subjects, the British, who were unjustly being tyrants over others of his subjects, the Americans) to be traitors, it was, arguably, an act of royal submission to Parliament's wishes: it was certainly the denial of the idea that one could be loyal to the King personally without being loyal to the British government as represented by Parliament, an idea that would be reinstated with the concept of Dominion status.
So, in conclusion, in this time-period Great Britain didn't have the conditions where either an American-style revolution or a French-style revolution was realistically possible there. That's not to say that a British revolution was impossible at all points in history (there have been multiple very famous English revolutions in history, so that would be an obvious fallacy) but I think it was so in this time-period, for the reasons highlighted above.