So if it chooses to have someone's head removed for spurious reasons it does in principle have the power (this would be an Act of Attainder, not used since the 18th Century, I think, and held to be so oppressive it's outlawed specifically in the US Constitution).
In practice, it's quite a lot more nuanced than that. Parliament is constrained by both politics (the public would be outraged by an Act of Attainder), international commitments (our EU membership, in particular, comes with supervening law which would make that a very costly action at a minimum), and historical practice.
The Facebook thing is a good example of these constraints. There's no question that Parliament could vote itself powerful and enforceable subpoena powers. And it has in centuries past. But it's also not used them recently, and done various other bits of legislating (e.g. the human rights act) which aren't compatible with arbitrary action. If the Commons tried to use its inherent power of imprisonment to enforce a subpoena, it might be overturned by a judge issuing a writ of Habeus Corpus on the grounds that the power is obsolete and in breach of the HRA. In principle, Parliament as a whole could pass an Act to prevent this, but it hasn't. So a lot of the checks that are constitutional in the US are conventional and institutional in the UK.
Finally, there are absolutely legal checks on the powers of the executive, which are enforced by the courts much as they would be in the US, though the source of these is basically law rather than constitution.
1) Parliament is supreme, not the PM. So extreme acts require the consent (in advance) of both the Commons (which has a built-in government majority but does sometimes have its own opinions - see Brexit) and the Lords (which can be unpredictable).
2) Norms are powerful in the Westminster system (sometimes in the form of so-called constitutional conventions) and surprisingly effective at stopping bad behaviour.
3) We've developed fairly strong judicial review, so the courts restrain illegal behaviour by the government. Although the law can be changed, it turns out this still stops a lot of abuses.
4) The evil PM would still have to successfully govern, which requires either the consent of the governed or massive force (at which point they'd need the active support of the military as well, and the military in Britain have stayed out of active politics since the 17th Century - another strong norm).
5) The Queen retains reserve powers, including the right to veto bills (she's theoretically the third 'house' of Parliament). She probably gets to do this exactly once before being deposed, and an attempted auto-coup is one of the more likely outcomes.
It's an odd system, but historically it actually works well. I spent some time interning in the US Congress expecting to find the system much better than ours, but I came away believing that a strong separation of powers in a Presidential system may create more problems than it solves.
Indeed they can, the Supreme court merely interprets the law. If congress decides to change the law then the Supreme Court's interpretation is moot.
These days changing the constitution is politically infeasible so it may seem this way - but ultimate power rests with Congress.
As the only body capable of updating the text of the law they have ultimate power. That they chose to constrain it was an altruistic act of a sovereign body. But only they (and their predecessor the continental congress) had the power to restrict themselves. The courts can only hold them to the text they themselves wrote.
The limits on the U.S. government exist because we put them in our organic law (the Constitution) which is not solely the prerogative of the federal congress (or any lone state).
Remember this the next time someone questions the fact we're a federal republic in the context of a short-term setback.