What the UK Election Would Have Looked Like Under MMP

New Zealand's political system is based on the UK's but there is one key aspect of it that we have moved away from (besides an unelected upper house of titled aristocrats of course). In 1993 New Zealand voted to switch from first past the post (FPP) used a mixed member proportional system (MMP) to provide proportional representation through party lists that people voted for as well as their electorate MP.
The UK still uses FPP with the make-up of the House of Commons being decided through 650 winner takes all elections across the country. Come election time people invariably bring up the inequalities of this system. In 2015 UKIP's 3.9 million votes netted them one seat while the DUP gained eight with 180 thousand votes. This happens as the candidate that gains a plurality of the vote in an electorate becomes their sole source of representation, even if most people don't like them.

UK Election 2017 - North East Fife Constituency 

Here the SNP candidate will represent North East Fife in Westminster even though two-thirds of the voters did not chose him.

The below results show this happening with the Conservatives gaining 48% of the seats even though they only 42% of people voted Conservative. This is not unexpected however, and is in fact a smaller disparity than their two previous vote counts.

UK 2017 General Election Results 

So what would happen if MPs were elected proportionally? The following table looks at how the seats would be distributed if it was done completely proportionally (with some rounding as we can't really have parties sharing half a seat each and only 646 seats as to not disrupt the proportionality).

Seats in the House of Commons allocated proportionally 

We can see that the Conservative seat share would drop, and the regional parties in favour of the nation-wide third-parties that struggle for seats under FPP due to their support bases being spread throughout the country.

Of course, this is not MMP which uses electorates as well as the party vote. MMP or Alternative Member Voting (using regional instead of country wide lists) is already in use in the UK in the Scottish and Welsh Assemblies. The following figures have been obtained using the Sainte-Laguë method, as employed in New Zealand and Germany, which uses a seat by seat allocation according to the parties' vote levels. A 5% threshold was also applied though an electorate win would get get around this.  
The UK would have to change its electorates for MMP to work. Germany, with 80 million residents has a 598 seat lower house with half the seats electorates and half lists though New Zealand has 71 of 120 seats chosen from electorates. It would be very difficult to predict how, say 325 UK electorates would vote however I think it likely that all of the parties who currently have seats would retain at least one apart from Independent Hermon. The Green's Caroline Lucas and Speaker Bercow have large majorities and I imagine Labour would happily stand aside for Lucas to get 10 more Green's in parliament. Halving the number of constituencies allows for a relatively insightful analysis as an overhang seat would only occur if Hermon retained a seat, though is the SNP had performed as expected there would have been an overhang.

Seats allocated according to the Sainte-Lague method.

The Conservatives would gain the most from UKIP missing out in this method though Labour, the Lib Dems and the Greens will also gain seats compared to the complete proportionality calculation according to their quotients. An explanation of Sainte-Lague can be found here.
As we can see a Conservative DUP grouping would only net 291 seats according to this and although Labour would only gain seven seats, a Labour, Liberal Democrat, SNP alliance would result in a 13 seat majority in return for their 50.4% of votes. Alternatively Labour could gain 333 with the Lib Dems, Greens and Plaid Cymru.

My calculations were greatly helped by Steven Kellow's Sainte-Lague calculator.