For what I understand Andrew Jackson was the first U.S. President to represent the common man, and to come from a humble poor background himself. He helped open the door to voting for all white males, not just landowning ones. Was there a British prime minister or leader that did something similar?
A direct counterpart, no.
Ramsay MacDonald was the first Labour Prime Minister and the first from a working class background. He was PM in 1924 and between 1929 and 1935. Whether he was the first to 'represent the common man' is complicated question, as what exactly does that mean. Do the various reform acts count?
I'd make the argument for Lloyd George to fill that role, specifically with his 'People's budget', he was middle class and was 'only' a solicitor. Lloyd George is probably more akin to FDR though (although FDR was 'posher.')