Fakenham is indeed a real place -- once voted 'the most boring place on Earth', according to Wikipedia. But Wiki does not mention any tradition of a fair being held there [the nearest is a recently established monthly Farmers' Market]; tho the song surely implies a traditional fair being held there? The name, tho, does possibly derive from Saxon for "fair place"; 'fair' in a different sense, obviously.

Semantic confusion all around, eh!

≈M≈