Gone for a Burton
Ii had understood that the phrase "gone for a Burton" a referred to the practice of laying out a dead body in an open casket (during a traditional wake). A man's body would be dressed up in his best suit, or one aquired. The firm Burtons being associated with cheap bespoke suits "going for a Burton" became slang for dying.
Pretty certainly not. If you go type Burton in the search box at the top you'll find some of our earlier discussions. The expression seems older than Burton the tailors.