1948-1949: Ernest Bevin (Labour) 1948 (Coalition with Liberals) def. Harry Pollitt (CPGB), Malcolm MacDonald (Conservative and National Labour), William Beveridge (Liberal)
1949-1950: Sir Vincent Tewson (Labour-Liberal Coalition)
1950-1956: Vic Feather (Labour) 1952 (Coalition with Liberals) def. Harry Pollitt (CPGB), Malcolm MacDonald (Conservative and National Labour), William Beveridge (Liberal), John Loverseed (Common Wealth), Frank Budgen (IWW)
1956-1962: Bill Wainwright (CPGB) 1956 (Minority with support from Common Wealth) def. Vic Feather (Labour), Reginald Maudling (Conservative and National Labour), Lancelot Spicer (Liberal)
1960 (Majority) def. George Woodcock (Labour), Reginald Maudling (Conservative and National Labour), Megan Lloyd George (Liberal)
1962-1968:Jeanne Hoban (CPGB) 1964 (Minority) def. Patricia McLaughlin (Conservative Workers'), Mary McAlister (Labour), Spike Milligan (Common Wealth), Donald Johnson (Liberal)
this is the 'Scottish election' to the general election list I did before.
Basically, in this world Attlee gets a bigger majority and the Communists do slightly better in 1945. In order to assuage his more left-wing backbenchers, an act is passed basically bringing the Boards of nationalised industry under workers' control, to an extent, as a great deal of management is done by the newly created National Boards Administration. An 'Industrial Congress' is established, essentially a state parallel to the TUC, but purely involved in the administration of nationalised industry. While for a time it is Labour dominated, the Communists soon infiltrate the unions and in 1956 are able to establish minority control of the Industrial Congress. This is one of the things that leads to Morrison's defeat in 1958 as he tries to reassert the control of the National Boards Administration and TUC over the Industrial Congress, causing an economic crisis.
In 1962, a referendum is held amongst the voting workers of the nationalised industries over whether or not to abolish the National Boards Administration and take up the Boards responsibilities in local and municipal government (which are quite considerable). Despite the Communists' majority, the workers' vote 'No' by a healthy margin. However, this vote put the Communists (and Common Wealth, the IWW and a few minnows) on the side of Yes, and the establishment parties of Labour, Tories and Liberals on the side of No. Labour haemorrhages votes, and in the 1963 general election, the Communists win almost 60 seats, primarily in areas of heavy manufacturing, but also in many coal mining regions. At the 1964 industrial election, Labour fall to third, while the rebranded 'Conservative Workers' Party' (a branch of the Tories specifically for industrial elections) come second. The Communists have lost their majority, but the Industrial Congress retains a majority for collectivisation due to the presence of Common Wealth.