Have you had an X-ray at least to confirm the severity of arthritis (the extent to which the cartilage and joint space are gone).
Unfortunately, if it’s not severe enough to warrant a replacement (and you’re under 60-65), physio and pain relief are realistically your only options on the NHS. There’s very little else, an arthritis brace might help, along with non weight bearing exercises. Strengthening, weight loss of needed.
The NHS can triage to orthopaedics if they feel surgery or perhaps a steroid injection only option. Unfortunately wash outs don’t offer much for arthritis, a locked knee a different matter.
Privately, you would be able to expedite seeing a consultant surgeon, a scan and surgery. Might be worth at least paying a few hundred for a consultation (try to at least get X-rays on the NHS and see a surgeon with an NHS practice locally too).
Private physio also an option if you’re not getting anywhere with the NHS.