this is my personal experience, it might not have worked for others but it has for us.
Book a private appt with the surgeon but he might need an introductory letter from your GP and the GP will charge but at least you get the choice of who you want to see.
When you go make it quite clear you only did this because of the pain you have and couldnt wait 5 weeks but you do not have the means to go private for the op, be honest and up front, usually this means you will be placed a little further up the NHS list also when the surgeon sees you with the NHS appt which you still keep, he will remember you and thats when they bring your op forward.
It might be classed as"cheating" but it happens every day and if you are in pain then do it.Hope this helps.