The government as it is, was elected by 100% of the vote. The party heading the Executive branch had fewer than 100% of the vote.

That is not the case. The government was elected with 33.7% of the vote.

You were trying to make a distinction between "government" and "executive" -- that's not how it works here, matey. His Majesty's Government is the party in power (or whichever grouping of MPs can hold the confidence of parliament), it is not all the other MPs - they are the opposition.

We don't have an "Executive". We have His Majesty's Government, they head all the departments, they command the civil service, they control the legislative timetable. The rest of the MPs and Lords are just plebs who get to vote on things. The opposition don't get to propose legislation, except when the Government feels generous and lets them (opposition days).

FPTP creates individual constituencies of roughly 70,000 voters, and the candidate who gets the most votes in one constituency wins a seat. The other candidates in that constituency get nothing, and all votes for them are completely wasted (unlike in other voting schemes). Candidates are usually a member of a political party. The party with the most seats gets first opportunity to form a government.

The 2024 general election was won by Labour with 9,708,716 votes (33.70%) out of 28,924,725 cast. Turnout was 60%, there could've been 48,208,507 possible votes.

The 2019 general election was won by the Conservatives with 13,966,454 votes (43.63%). 2017 was 42.3%. 2015 was 36.8%. 2010 was 59.1%. 2005 was 35.2%. 2001 was 40.7%. You can see the last result was the lowest vote share in decades.

And yet, 33.7% of the vote nets you 100% of the power. Thanks, FPTP!