Yes, you can apply for the REPS qualification. I think the Basic qual gives you the equivalent to a Physical Trainer in civvi street (REPs 2), but I could be wrong.
Go onto the British Army website, find the APTC pages and follow the links to REPS. Regular PTI's can get the annual fee (£25 ish) paid for via the APTC, don't know about the TA, try contacting your Bde RTC, the SMI APTC will have info.
Onthebus is bang on. You can join REPs for £25 p.a. as level 2 with quals in circuits and gym. However to maintain REPs status you will have to attened seminars or training courses to get acredited learning points. 12 a year for level 2. Usually 4 a day per course etc. The industry pay a poor wage though, the money is in private training