In the 2015 General Election UKIP got 4 million votes, but only one MP if I recall correctly.
Under the AV system, I wonder how many MP's they would have got and would they have had enough influence to change any of the outcomes?
They would have needed lots of electable candidates. When you look at the people involved in UKIP and those who actually stood, you'll realise they were never going to be elected. For all his talked about popularity, Farage himself couldn't get elected as an MP.
You are discounting the vagaries of alternative voting systems Nick. Look at the numpties that get elected to the Scottish and EU parliaments.
Farage for example.
But you're ignoring the fact that to form or even influence a
government takes more than a couple of
freaks charismatic, narrowly focused, niche politicians that somehow managed to get elected. Look at the Green Party; its manifesto is hardly niche even in the UK, but after many years of high profile campaigning has one elected MP, and two Lords. As far as parliament is concerned, they're utterly insignificant. Our +/- 2 party, first past the post system emphasises this effect, but it's also true where proportional representation or other methods are used.
The eleven Lib Dem MPs might be enough to just swing a majority if required, especially as many current centrist Tories really ought to be Lib Dems if ambition wasn't clouding their judgement; Boris Johnson is a good example.
UKIP achieved its aims by using popular (but not electoral) support to hammer a wedge into already existing cracks in both Labour and more significantly Conservative parties. It's very nature was never going to survive a Leave result.