In the UK the Queen passes the laws, so there seems no reason she couldn't issue a writ making particular actions of MPs unlawful.
Presumably she doesn't because she rather likes the money and the palaces more than she wants to settle the question as to how you have a parliamentary democracy and monarchy with "you don't".
I don’t know if that is even possible within the confines of the UK’s latter-day (uncodified) constitutional monarchy, but the Queen resuming the practice of unilaterally imposing laws upon Parliament and the Realm at large would be one of the most terrifying regressions of the past several centuries.
Besides, the scenario you depict further reinforces my argument that there’s a “trusted root” at the apex of our democracies and that this entity (whether the Queen, or Parliament, or Congress, or the President, or whatever-have-you) can pursue its own interests with abandon, and there’s nothing we buggers further down the pyramid can do to prevent it.
If the Queen imposed a requirement for MPs who sponsor laws to go to prison if those laws clearly beach the ECHR (or maybe HRA) who'd complain?
It's far less terrifying to me that the present Queen can do that than that any oligarch with a £100M to spare can probably "lobby" to get the changes they want.
The royal family are in a dicey position, but I trust the current Queen more than MP s in general, but perhaps less than the 2 Houses as a whole. She can probably do anything that goes with either Parliament OR with the demos but couldn't go against both.
Presumably she doesn't because she rather likes the money and the palaces more than she wants to settle the question as to how you have a parliamentary democracy and monarchy with "you don't".