I don't know why people are saying it's not possible to jump the waiting list, I've done it twice.
The wait for an appt with an ortho consultant was monstrously long here. We have insurance through work which is very basic, but will refund you 50% of the fee for a consultation with a specialist. In 2012 I got a very quick private appt with the surgeon I'd been referred to by my GP, who had a 12-month waiting list at the time. He added me to his NHS list straight away, knocking a year off the waiting time. I had had the surgery I needed long before I would have even seen the surgeon if I hadn't seen him privately.
In 2020, I did the same with a different ortho consultant, after having been royally pissed about for 18 months by a combination of Covid, the complex pathway for for ortho referrals and the woeful incompetence of the phsyio service that couldn't organise a piss-up in a brewery. He added me to his list for NHS surgery in December 2020 and I had the op last October, around the time I would have had my first appt with him.
I felt dreadful for doing it, it goes against all my principles, and consider myself to be a total hypocrite for doing so, but I was in bloody agony and, the first time, I was on absence management at work because I was having so much time off.
And just to make me feel even more guilty, the second surgery was carried out in a private hospital but paid for by the NHS, because they were desperate to reduce the waiting list.