Here's what to listen for:
The th/θ has a slight hiss and sounds sharper, whereas the f is slightly muffled and puffy. Think of the θ as an s which has slipped forward, not an f which has slipped back.
By the way, there is a British accent in London (nooo, not all of London) which has replaced θ with f, so "south" sounds like "souf", and "three" sounds like "free".