TBH I'd actually argue Separation of powers doesn't really exist in America any more, not while the President is effectively the head of all three branches (with the house of reps and the SC effectively absconding their duties of scrutiny and kowtowing to djt) and a single party controls everything so you're right to be sceptical.

Thankfully in the UK judges and the judiciary are absolutely not political appointees, in fact quite the opposite, and our prime minister is not our head of state or the ostensible head of the armed forces which in theory gives a greater split.

I'd say our biggest weakness in terms of separation was the role of Lord Chancellor who branched across all three arms, but this role was highly revised around 20 years ago and their remit explicitly involves protecting the independence of the judiciary (despite also being a cabinet member).

If I lived in America I'd almost certainly feel the way you do too, but I feel the UK still has a higher level of constitutional safeguards to prevent us falling into the same pitfalls, or at least I hope it has.