The british political party that emerged during the 1920s as the champion of the working class and the main opposition to the conservative party was the

Labour Party

Explanation:

According to my research on the British Political Parties during the 1920's, I can say that the party being described within the question is the Labour Party.  This party is a  centre-left political party, that usually share ties with social democrats, democratic socialists and trade unionists.

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