Faggot has a range of meanings in British English.
First of all it is something you eat. The biggest supplier of faggots is a company called Brain, so Brain's Faggots is part of the language:
Mr. Brains 4 Faggots In Rich Sauce 378g product information - Tesco.com
It has a host of other harmless meanings. For example many rural dialects use faggot for a bundle of fire wood. Faggoting is an embroidery term, so it is a word great aunt Maud might use.
There's also public school use of the word (public=private). A fag or faggot is someone who does jobs for a prefect, which is part of the fag system. I suppose this is the origin of the sexual meaning, but its older (harmless) meaning hasn't entirely been lost. And in the UK a fag is a cigarette. Faggled out (tired out) is completely non-sexual.
Is faggot funny? Maybe. It all depends on the context. It certainly can be most offensive, but often isn't. And there has to be humour in Brain's Faggots.