You're entitled to ask for a referral for specialist treatment on the NHS.
But whether you'll get the referral depends on what your GP feels is clinically necessary in your case. Your GP also generally understands your health history and treatments better than anyone and will base any decision for a specialist referral on this knowledge.
If you ask your GP to refer you to a specialist, they'll probably suggest that you first try various tests or treatment options to see whether your condition improves.
Generally, you cannot self-refer to a specialist within the NHS, except when accessing sexual health clinics or A&E treatment.
A specialist will only see you with a letter of referral from your GP.
The letter will give the specialist essential background information, such as your medical history, and it'll also contain details that the specialist needs to pay particular attention to.
If you want to see a private specialist, you're still advised to get a letter of referral from your GP.
When doctors write to each other about your care, they should aim to give you a copy of their letters or emails.
If you do not get a copy, you can ask for one.