You are entitled to ask for a referral for specialist treatment on the NHS. However, whether you will get the referral depends on what your GP feels is clinically necessary in your case.
What happens when you are referred by your GP to see a specialist? – patient leaflet
If you ask your GP to refer you to a specialist, they will 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 accident and emergency (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 will also contain details that the specialist needs to pay particular attention to.