The House of Stuart was the last reasonable chance for an Executive Monarch. If the Royalists had won the Civil War and the King granted control over annual revenues (rather than Parliament controlling annual levies), then maybe, for a while, this might be possible.
I doubt even then. The King would have had to make some sort of concessions and he probably wouldn't be given cart blanche for new and exceptional taxes (for war for instance). They'd eventually claw power back.
Basically the POD would have to be further and further back. I'm not sure when would be a good time to turn Britain into a "French-Style" autocratic monarchy. Perhaps before the reformation. Even Catholic "absolutist" nations like Austria and France usually had plenty of constraints on power by regional parliaments, especially the purse-strings.