In the Fifties and Sixties there were Variety Shows where the host (for example, Dean Martin) would mix humour and music, but without the darker satire that makes Cabaret cabaret.
After that, the music and the humour split, with Stand-Up comedians preferring not to sing, and Musicals preferring not to make too much social commentary. There are still musical bands that contain satire who describe themselves as Dark Cabaret; these include the Tiger Lillies and the Dresden Dolls. And then there are the musical comedians; for some reason people think Tim Minchin is funny.
But maybe the best example of English-language cabaret is the Muppet Show?