The absence of a strong constitution protecting fundamental rights is also an issue. With a 50%+1 majority, the house of commons can vote pretty much any law it wants with no counterpower.
The British system is, indeed, fundamentally insane, from a technical perspective. They nerfed aristocratic power by neutering the House of Lords, but didn't bother replacing it with some other check or balance, leaving the Commons all-powerful - and with an electoral system that disproportionately favours cohesive ideologic minorities. Ironically, this was largely done by self-declared leftists, who utterly failed to anticipate how fascism could easily manifest through such a system.
> Parliament Act 1911 was passed by a Liberal Government
... sustained by Labour MPs, and mostly in order to bust a ironclad Tory majority in the Lords that was effectively "ruining" every progressive bill.
It was then further strengthened in 1949 (Lab) and 1999 (Lab).
I mean, there is no shame in this: it was a worthy and progressive cause to drag a XVIII-century model (kicking and screaming) into modernity. It's just a shame that the execution was fairly poor, particularly in 1999 - when there was a unique chance to build something more theoretically sound, and (unlike 1911) there was a lot of history to learn from.
This is useful context, however I wanted to make clear it was the 1911 Act that made the supremacy of the Commons; as you say it was further strengthened in 1949, by shortening the veto timescales.
Labour's position changing from 'abolish the house of lords' originally, to 'get rid of some hereditary peers' in 1999 was incredibly poor, as you say.
It's not that "they're turning", it already happened. Tony Blair and Bill Clinton shared political platforms almost precisely.
A recent effort to go "back to their roots" (the Corbyn years) ended with a stalinesque purge of such leader. Sadly this leaves free reign for upstart neonazi and neonazi-adjacent parties (BNP, UKIP, Brexit Party/Reform UK...) to rip through traditional Lab heartlands.
> Tony Blair and Bill Clinton shared political platforms almost precisely.
I think this needs justification. There is no evidence that Clinton has ever been in favour of socialized healthcare for example, investment in which was a major tenet of the Blair platform.
> The British system is, indeed, fundamentally insane, from a technical perspective.
The best is the unwritten rules. Which are ironclad and “part of the constitution of this country”, except when they aren’t and get just ignored because it’s convenient. But hey, every couple of years journalists can play fun what-if games tracking down ancient customs and speculate whether a 300 years old precedent could be used to behead the PM or some other nonsense.
While in theory you are correct the reality is somewhat different. Individual mps are beholden to their local party and would hesitate to vote on anything that may endanger their position. Backbenchers have brought down 3 successive governments. There also exists an upper chamber and a high court to appeal to. It's mostly a pretty stable system.
Individual MPs are not selected by local parties anymore, that ship sailed 30 years ago. Parachuting chums in safe seats it's been the accepted norm since (at least) Blair. Backbenchers do what they do because they're fighting among themselves, organized in gangs (sorry, "think-tanks" or "research groups") to bolster their own career opportunities.
There is no upper chamber that I know of (the Lords is legislatively dead, a strong government can simply ignore it), and the powers of the High Court, already diminished by recent reforms, are likely to be further curtailed very soon (read the tea leaves: the debate on "abusing judicial procedures to make law", once the remit of right-wing Americans, was the subject for an entire Reith Lecture cycle only a couple of years ago; after the Brexit saga, Tories will take an axe to the HC as soon as they can afford to do so).