DISCLAIMER: this is a for-fun thought experiment, and remember that if PR was used in real life, the voting tactics would be much different (actually, the "tactics" would be near non-existent, people would vote for who they like--yeah, I know, novel concept) and thus the results would also be different.

DISCLAIMER 2: I don't advocate a party-list PR system. There are others available, like MMP or STV. They're way better than the FPTP system used in the UK and US (and other countries). But for the purposes of this thought experiment, a simple PR system is assumed.

Using a d'Hondt calculator I found on the internet, I was able to calculate the number of PR seats each party would get in a 650-seat parliament. Here is the list (the seats they have in real life are in brackets):

Tories ---- 244 (331)
Labour --- 201 (232)
UKIP ------- 83 (1)
LibDems -- 52 (8)
SNP -------- 31 (56)
Greens ---- 25 (1)
DUP --------- 3 (8)
Plaid --------- 3 (3)
Sinn Fein --- 3 (4)
UUP (+ind) - 3 (3)
SDLP -------- 1 (3)
Alliance ----- 1 (0)

Overall, it's bad for big parties (Con, Lab), great for smaller parties (LibDem, UKIP, Greens), bad for large regional parties (SNP, DUP), and inconsequential for smaller regional parties (Plaid, UUP, etc.).

As I will always say, it's good for democracy. Whatever you think about these individual parties, it's never a bad thing to see the people's views represented more proportionally, and certain views neither magnified nor suppressed by anomalies in a flawed voting system.

Now, to step off of my soapbox and analyze those numbers: the Tories would, almost undoubtedly, retain power with these numbers.

I'll show my work: even if you added up Labour and all of their possible friends (LibDems, Greens, SNP, Plaid, DUP, Alliance--I'm calling them the "Anti-UKIP Coalition") it's only 317 seats. In fact, even if you added up the Conservatives, LibDems, DUP, UUP, and Alliance in a coalition reminiscent of 2010-15, it's still just 303 votes, of course short of a majority.

Although, realistically, my teaser that Farage would be Deputy PM is also erroneous. The Conservatives would most likely run a minority government, reaching to the center to get LibDem and Labour suppport for some things, and reaching to the right to get UKIP support for other things--like the EU referendum, but Nigel and his buddies wouldn't have influence beyond what the Tories agree to. So nothing too crazy would get passed.

Conclusion: I may have done some harm to my viewpoint that FPTP needs to go by highlighting how well UKIP, a party most of you loath, would've done, so I need to remind you of this: it's a case-by-case deal. In other years, the Greens would have the tremendous result. The point is this: a government that represents the views of the people is better than one that only represents two views (plus a regionalist party) with barely any representation whatsoever for significant minority opinions, such as UKIP and the Greens.

And yes, this would mean more coalitions, but a parliament/congress where members are forced to compromise and create laws multiple ideological groups can get behind sounds a lot better than what you have in Britain, where a party that gets only 30-something percent of the vote has over 50-percent of the seats, and doesn't need to answer to that natural system of checks-and-balances that exists in governments with several large parties.