Adopting Proportional Representation would give smaller parties in the UK, such as the Liberal Democrats, the Green Party and UKIP, the chance to gain more seats in Parliament.
Currently, although many small parties collectively gain a significant share of the vote, they receive far fewer seats than the two larger parties, due to the electoral design. For example, one study has shown that in the 2019 UK election, 16% of the vote share (5.2 million votes) was won by the Green Party, the Liberal Democrats and the Brexit Party, however they received just 2% of parliamentary seats.
This was even more marked in the 2015 election, where the Greens won 1.1.m votes and UKIP 3.8m, yet both parties only sent one MP to parliament.
The current first-past-the-post system also means that the amount of votes needed to elect an MP from each party is wildly variable depending on the size of the party. For larger parties such as the Conservatives and Labour, in the 2019 election, they required 38,000 and 50,000 votes to elect an MP respectively. In stark contrast, it took 800,000 votes to elect one Green MP, and although the Brexit party received 600,000 votes they received no MP. 
Smaller parties in Parliament mean a greater diversity of political opinion. With Proportional Representation, the smaller parties stand a chance of having a greater number of representatives elected to parliament, and therefore they stand to influence policy making and debate in a way currently out of reach.