looks

If I understand aright what's going on, I don't believe that that's a constitutional crisis.

https://www.npr.org/2023/11/15/1213147180/uk-supreme-court-rwanda-asylum-policy-sunak

Following the ruling, Sunak said in a news conference Wednesday evening that he would "pass emergency legislation" to deem Rwanda a safe country and that he would "not allow foreign courts to block the flights" the U.K. plans to use to transfer migrants to the African country.

So, he's not rejecting the ruling, but rather saying that he'll have Parliament pass a law to permit it, which will simply render the ruling ineffective.

Here in the US, the Supreme Court has the power of judicial review of federal laws; they asserted this power in Marbury v. Madison -- which was a constitutional crisis -- and it wasn't disputed. That produced a lot of why the US works the way it does today.

https://en.wikipedia.org/wiki/Judicial_review_in_the_United_States

So, SCOTUS can say "Congress has done something unconstitutional". That invalidates the law. There's no direct recourse the President or Congress has to override that.

That's not how the British system works. The Supreme Court in the UK can say that the executive has done something that conflicts with British law. But it has no power of judicial review of laws that Parliament passes -- it cannot invalidate laws Parliament puts through. Because the Westminster system is a parliamentary system rather than a presidential system, because the Prime Minister is chosen by Parliament, the two are generally in accord. So if the Supreme Court says "what the executive is doing is illegal", the Prime Minister can generally just have Parliament pass a law to make it legal.

There is no constitution in the UK separate from any law that Parliament might choose to pass. A simple majority in the House of Commons -- technically the King-in-Parliament -- is the absolute power in the UK, is where sovereignty is vested, whereas in the US, it is vested in the US Constitution, where the bar for constitutional revision is three-quarters of US states.

So in practice, the Supreme Court in the UK has much less ability to limit action of the British executive than SCOTUS does over here. It can really only do so if the executive and Parliament are in disagreement as to the proper course of action.