No political party since 1931 (under the First Past the Post electoral system) has won over half of the electorates support in a general election in the UK. The introduction of mandatory voting would increase participation making it likely that one candidate would receive a majority of the electorates support. This would address the lack of democratic legitimacy at the heart of the UK political system.
There are other ways to increase democratic legitimacy in the UK political system that would not require forcing people to vote, including introducing a proportional electoral system, devolving power to the nations and regions, and allowing the electorate a greater say in selecting the candidates for prime minister.
[P1] The UK government is not typically overseen by a party with a majority share of votes. [P2] This decreases democratic legitimacy. [P3] Mandatory voting would increase democratic legitimacy by making it more likely one party will gain a majority share of the votes.
Rejecting the premises
[Rejecting P3] There are more effective ways to increase democratic legitimacy.