What is First Past the Post and how does it impact electoral outcomes?

The majoritarian British electoral system of First Past the Post (FPTP) is a Single-Member Plurality voting method used to elect members of parliament to the House of Commons during five year fixed term general elections. The system geographically divides the United Kingdom into 650 constituencies, each of which gain representation by one candidate which receives the plurality of votes in its constituency.
An indication of how the British electoral system is broken is the disproportionate representation single-member plurality produces. Disproportionality can be recognized using a Gallagher index which captures the difference in percentage of votes a party wins versus the percentage of seats it wins. In the 2015 general elections, disproportionality was blatant as conservatives won 36.9% of votes and 50.9% of seats indicating they were 14% over-represented, whereas, UKIP won 12.6% of votes and only 0.2% of seats revealing they were 12.4% under-represented. The overall UK election of 2015 generated a Gallagher index of 76.8% which, according to the threshold of 85% or above representing proportionality, revealed that the results were disproportionate to electoral votes. During the 2017 general elections, although the Gallagher index increased to 90.5% exceeding the threshold, due to the increased two-party structure in which 82.2% of votes and 89.2% of seats went to the Labour and Conservative party, the outcome was still not representative of the body of voters as the Conservative party now dominates government with a minority of 42.2% of votes. This undermines disciplines of representative democracy as the government is not symbolic of even half the electorate.
FPTP also leads to regionalism where geographically concentrated parties gain disproportionate advantages in seats. For example, in 2015, UKIP got 4 million votes and 1 seat whereas SNP got 1.5 million votes and 56 seats because of SNP’s intense support focused in Scottish constituencies. FPTP undoubtedly penalizes smaller parties such as UKIP and the Greens and rewards larger parties such as Labour and Conservatives. The bias of representation in favor of larger parties was prominent in the 2015 election whereby if the Greens 1.2 million votes were combined with UKIP’s votes, the collective number of votes of the two smaller parties would be greater than 5 million which was more than half of the 9 million votes won by labour, however labour won 232 seats and the Greens and UKIP between them only gained 2 seats. Similarly, in 2010 labour won 29% of votes and 258 seats and liberal democrats only got 6% less votes but an inequitable 201 fewer seats.