This article uses Sartori's classification of party systems to map changes in the post-war UK party system. Using measures of the effective number of parties and of parties' policy positions, the article shows that ‘classic’ two-partism from 1950 to 1970 broke down amid ideological polarisation. This development created a ‘vacated centre’, which the Liberals filled, leading to fragmentation of the electoral-party system. This period gave way in 1997 to one in which ideological convergence returned, alongside further electoral fragmentation. The uneven decline in the vote shares of the parties finishing first and second led to supermajorities and two long periods of single-party rule from 1979 to 2010. The article argues that the UK had an alternating-predominant party system in this period. This system was a hybrid of single-party predominance and classic two-partism, in which competition between the two main parties was usually very weak but where there was some scope for governmental alternation.