As one who’s witnessed a change from FPTP to PR in his own country, I feel more or less obliged to comment on this.
Here in NZ we're just coming up to 30 years of PR, after a couple of referenda in 1992-3 gave a decisive mandate for the change from FPTP. On the whole it’s been a distinct improvement on the “elected dictatorships” that tended to prevail under the old system. For one thing, we no longer see anomalies like winning the popular vote, but still not getting enough seats to govern, something which happened in both 1978 and 1981.
In the form of PR adopted here, though, there’s still plenty of room for political shenanigans. It's very similar to the one used in Germany: we call it Mixed Member Proportional (MMP). The details of how it operates are too complicated to go into on this forum; those interested can look it up on Wikipedia or elsewhere –
this site explains it quite well and succinctly.
However, I don’t know to what extent the NZ experience is relevant to the UK. For one thing, we have no second chamber in our parliament. For another, there are seven Maori-only seats in the House, plus a sizeable (though currently unstable) Maori political party which is only partially comparable with the various nationalist parties in the UK.
Under MMP, many minor parties have appeared and disappeared in the last three decades, usually founded by disaffected sitting members of the two major parties (centre-right National and centre-left Labour). Some never had a hope; some flourished briefly before being consumed by in-fighting or scandal; others again were effectively one-man-bands which did well for a time, sometimes even making it into government, but which vanished soon after their founder/leaders died or retired. Only three have had real staying power – the Greens, the hard-right ACT, and New Zealand First, the most successful of the one-man-bands, which still might just manage the transition to a regular centre-ish party once its now 80-year old founder/leader exits the scene.
The most tiresome feature of this (or I suppose any PR) system is that one of the lesser parties can become “king-maker” in deciding which of the two big parties it’ll go into coalition with, and thus achieve a disproportionate degree of influence on policy. Right now that role is filled by NZ First. Whatever policies this outfit espoused when first set up, it seems now to have no bedrock principle at all beyond getting itself into office. It’s twice been booted out of the House altogether after contentious spells in coalition, only to reinvent itself and somehow squeeze back in again. It’s currently riding a populist wave to achieve its highest ever standing in the polls at around 15%. Given its indifferent track record the phenomenon is hard to explain.
Tactical voting most certainly operates too. The ACT party only survived at all for many years because National effectively gave them a free seat in the House. ACT’s leader stood for an electorate seat, and National repeatedly kneecapped its own candidates there by encouraging their members to vote for the ACT man instead - their reasons for doing this are too involved to go into here. (They did the same in one of the Wellington seats as well in the first MMP election in 1996. A documentary about the campaign in that electorate showed the defeated National candidate calling his leader a "f***ing prick" on camera.)
The Electoral Commission, which oversees the system, has more than once recommended some significant changes to it, which make a lot of sense to most, but which the government of the day has almost invariably ignored, because they happened to benefit from the arrangements as they were.
Quite a lot of folk here are distinctly cheesed off with all the PR political ballet, and still seem to hanker for the good old days of two parties taking turns to govern with a clear majority of seats. At the 2017 election, there was near-outrage in some quarters when the biggest party – National – was excluded from office after NZ First opted to go with Labour. To them it was almost unnatural that the party having the most seats didn’t get to rule. Still too early to say whether that old-fashioned mindset will gradually disappear.