Usually a painless click deep in the hip is a tendon passing over a bone like your physio said - harmless enough. The usual suspects are gluteus maximus or psoas. I wouldn't worry about it.
Is the physio treating the muscle but not the cause? Muscles usually get tight to compensate for a biomechanical problem elsewhere and are rarely the primary cause of musculoskeletal dysfunction. 20 weeks is a heck of a long time.
I'd go. If he's trained with Premier, he's not a state registered physiotherapist (MSCP) because he hasn't done the pre-requisite 3 year degree. But MSCP's straight out of university haven't had very much exposure to musculoskeletal problems and tend to add things like that (and manipulation) on post-grad if they are interested. This means that they will have had a good few years of general physio experience to add to their skills too. Premier train sports therapist, personal trainers etc and have a very good reputation. I would check his qualifications re: manipulation though, it's not something to be played at.
(Declaration of interest: I'm just about to qualify as an osteopath after 5 years of very difficult university training and don't like to see all these things lumped into one bag!)