I've got a finger injury. It was initially seen through A&E/minor injuries and the referred to the hand trauma unit by A&E.
Since then, in 8 weeks, I've had 2 other hospital appointments and 5 sessions of physio. If I'd tried to do it via GP, I'd have waited 4 weeks for the first appointment and way more before an inital physio appointment.
I don't know if I did the right thing for the system or not, but it was definitely the right thing for me and my finger.