LONDON — In 1900, a Jewish Lithuanian immigrant named Meshe David Osinsky arrived in Britain alone at the age of 19. He set up a clothes-peddling business, adopted the name Montague Burton and then opened a tailoring store in Chesterfield, a northern industrial town.

By 1939, Burton had 595 retailers across the country offering made-to-measure suits for men. By the time World War II broke out, the company made a quarter of all British military uniforms and a third of demobilization suits (issued to soldiers returning home), making it the affordable brand it remains today.

Just in time for the men’s wear season, his story is one of dozens finally being told in “Moses, Mods and Mr. Fish,” a small but powerful exhibition on display through June 19 at the Jewish Museum London, in the borough of Camden Town, which aims to document the role of Jewish designers in shaping the male wardrobe over the last century, including Moss Bros. and Marks & Spencer.

While the show is rich in photographs, video footage and advertising campaigns, examples of the suits themselves are relatively few.