I think you’ll have to make sure you have sufficient supplies of Gilenya before you come to the U.K. (I’d aim for a few months worth if you can get it). Then when you arrive in the U.K., register with a GP. This is a general practitioner - you’ll find your local surgery depending on where you move to on line. Make an appointment to see the GP as soon as possible and ask for an urgent referral to a neurologist.
If you can, get copies of all your diagnostic tests before you come to Britain, especially copies of MRI scans. You’ll perhaps need a letter from your current neurologist (translated and the original) to pass on to the British neurologist. That way you’ll get your treatment expedited.
Theres no point in recommending a neurologist. Depending on where you end up living in the U.K., the most important thing is to get to see a neurologist - any one - and prove your diagnosis and current disease modifying drug.