I do not know what you're on at the moment, but if you're on narcotic type of analgesic, I think obtaining a medical would be difficult.
I stand to be corrected, but I think Diclofenac (I believe this is prescription-only) is NSAID, and help with rheumatic conditions. I do not know whether UK CAA would allow this or not, but maybe it's worth discussing the matter with them?
Also Ibuprofen, also NSAID should not be a problem as this is available over the counter and is classed not disimilarly to Paracetamol in terms of its' 'strength' so to speak.
Also, Australia seem to have slightly different policy in terms of the use of analgesics. I know it's far away from where you are, but maybe you would like to look into it? See CASA's website on
www.casa.gov.au. I know that they allow up to 15mg codein combined with say paracetamol.