The big three that come to my mind are:
Everton, 'the people's club'. Not only in a Labour area but also is known for valuing community in a way that some would describe as left-wing.
Arsenal known for having Labour-supporting fans. More the trendier London type of lefties (like Corbyn, who supports them), than the grittier Northern ones. A lot of left-wing opposition from fans over the pay of its workers lately.
Celtic. Associated with Catholicism/possibly Irish nationalism, which is generally espoused by leftists.