The UK political system is a multi-party system. Since the 1920s, the two largest political participation have been the Conservative Party and the Labour Party. Before the Labour Party rose in British politics, the Liberal Party was the other major political party along with the Conservatives. While coalition and minority governments have been an occasional feature of parliamentary politics, the first-past-the-post electoral system used for general elections tends to maintain the dominance of these two parties, though each has in the past century relied upon a third party such as the Liberal Democrats to deliver a working majority in Parliament. A Conservative-Liberal Democrat coalition government held office from 2010 until 2015, the first coalition since 1945. The coalition ended following Parliamentary elections on 7 May 2015, in which the Conservative Party won an outright majority of 330 seats in the House of Commons, while their coalition partners lost all but eight seats.

Can we conclude that does the uk have a two party system?
no