A resource to consider (although not medical referrals) is through the UK Acquired Brain Injury Forum's directory of rehab services --it's on the web, easy to find.

That could identify service providers who are geographically close to you. From a conversation with some such provider, you find identify a suitable neurologist.

Secondly, in your shoes, I would try to reach two people who aren't neurologists but might be extremely helpful --

Tom Manly, at Cambridge's Cognition and Brain Sciences Unit -- he's a very long-established psychologist, well-experienced in rehab, academically well-versed, + does detailed neuropsych assessments expertly (but I'm certainly not seeking to sell his services at all!)

Andrew Bateman, at Ely's (NHS) Oliver Zangwill Centre for Neuropsychological Rehabilitation -- (or one of his senior colleagues) -- he's director at research and approachable (as are his colleagues, I believe).

You can easily trace their emails and phone numbers on the web.

They (or colleagues) "in the know" may be able to direct you towards a neurologist.

... In the situation you sketch, having presumably had a concussion some while ago, but being unable to firmly attribute current signs and symptoms to the concussion and/or other causes, IMO a medical neurologist will be less helpful than a neuropsychologist. The latter could test/assess you and compare your pattern of results to the situations for "typical" PCS individuals. A UK neurologist will almost certainly just refer you for neuropsych assessment, possibly charging you lavishly in the process and delaying matters too.

Anyway, sorry to offer an opinion if it's intrusive or meddling -- but most of all, good luck.