In reply to ad111:
From the limited description,rotator cuff seems reasonable.Can you put the hand on the affected side right up your back as usual? If no,it may be something else.
Have a look at shoulderdoc.com,I think that is its name.
Go two pronged,NHS and private. You can't expect your GP to just book an MRI.He has to refer you to a shoulder specialist (orthopaedic consultant or specialist physio),who will examine you and may or may not plan MRI.Either way,you won't get MRI on your first trip to hospital.You could typically wait a few months for appointment and a few months for MRI....and a few months for e.g. an operation if needed.
In the meantime pay to find a good physio to help.Be prepared to change physio if it doesn't thrill you with confidence. Months without specific exercises=extra months of recovery.
I had a shoulder injury requiring physio,a daycase procedure (but not an operation) and lots more physio.All in it took a year to sort.The person who can influence your recovery most is you.MRI,seeing specialists and even operations are the small parts; regular exercises loads of times a day every day is the way out of this.
I suspect this will degenerate into a thread about NHS waiting times!
Good luck!
Post edited at 11:31