I agree with corbyloon, I used to deal with liability claims in a previous role. The only way you would stand a chance now is if a) the accident had been recorded and witnessed in the accident book at the Gym, or wherever it happened, b) if there was public liability insurance covering the instructor - was he private or employed at a gym, is he still around? c) you sought medical treatment straight away (which you did, so that will still be on record) d) you didn't realise until now that that you had a permanent disability from the accident. The Statute of Limitations says you have to claim within three years of the accident but I recall as CL says that it's three years from your becoming aware of your lasting condition as a result of it. Have a look here
http://www.thelegalli...-bring-your-claim.htm but your best bet would be to consult a solicitor now, for a opinion. In theory you are out of time, but the time bar can be extended under certain circumstances, IMO.
Whyever have you left it so long before doing something about it?