That's not the way it worked with me, one time I had an urology issue which needed to be referred to a specialist, my doctor gave me a choice of hospitals, then again when I had an ENT issue I was given a choice of hospitals but my doctor wrote to them directly to refer me. 
I was referred to two hospitals for Urology, the second by the first because they were not equipped, kicked up with the GP, did some homework, picked the hospital myself, there might be a referral in it, but I was free to choose any specialist hospital.
Same with muscular and skeletal, only this time a private hospital was listed too, one I have been to before and my GP had already recommended the consultant, so I chose that one, but only got it by phone, not offered online.
Each time I was given an access code and was free to choose any hospital suitable, anywhere in the country.
I think a lot is dependent on your GP, and if it is a multi surgery business you are unlikely to get joy, it probably effects the profit margin

but an old family type practice you may.