Reachesme may have hit on something but I never heard the term 'faggot' (to mean a gay man) until about 30 years ago, and then it seemed to come mainly from U.S. films and TV.
When I was a child, 'faggot' (as applied to a person) had quite a different meaning, and was nearly always prefixed by "miserable old...", and it meant a disagreeable middle-aged or elderly woman. Also, where I lived (Sussex) faggot usually meant a bundle of sticks used for kindling, rather than the meatball usage. At the same time (late 1950s) the normal colloquial terms for gay men were queers or (sometimes) fairies, but the latter term would probably only refer to the 'queenish' type.