What makes you say that about the UK? As an American, I’ve always been envious of what I perceive as the UK’s greater electoral flexibility, expressed through systems like snap elections and Parliament’s role in appointing the chief executive.
Same problems as the US. We have a two party state, which means very broad coalitions, no real choice, and a lot of unheard voices. Just like the US, we have suffered deindustrialisation as companies shipped production overseas, encouraged by our politicians, and those people who lost out have no way of fighting back. Their resentment has grown to the point where it is now finding expression through Brexit and populists like Nigel Farage and Boris Johnson.
Proportional representation provides a "release valve" for angry minorities, in that new parties can form. Some people think this is a danger, because they see those parties gaining some real power, but what usually happens is their supporters see the realities of political compromise, see some gains, at least feel represented, and the anger recedes.
The first place we're seeing the cracks is the UK leaving the EU whilst NI has not, and support for Scottish independence on the rise.
More pertinent to your reply: without a constitution the flexibility is simply exploited for party political gain, which often destabilises the country. Similarly, the trend has been in recent decades for the executive to increasingly take power away from parliament, which has proceeded unchecked. So some of us envy your constitution and the lack of gaming in e.g. the timing of elections. And let's not even get started on the "ceremonial" royal family...
I suppose what I mean is that I like how this process produces PMs who are aligned (at least to start) with the majority will of Parliament, since the party/coalition with the most seats in Parliament gets to pick them.
In contrast, US Presidents are elected with zero input from Congress and are often at odds with the House and/or Senate majority.