Which medical school you go to won't directly affect your future career as a doctor or specialty recruitment - the NHS is the only provider of graduate medical training posts in the UK and takes the GMC's stance that all medical schools are equal - going so far as to blind recruiters from which medical school you graduated from to ensure there is no bias. Your medical school I understand is only checked after you are made an offer to validate that you did indeed graduate from medical school.
Therefore, you need to choose the medical schools you apply to based on a) which
you are mostly likely to be shortlisted for interview at and b) which have the course format/location/other facilities available you are looking for.
For a) you need to research the different shortlisting methodologies of different medical schools to understand how they shortlist. Some weight GCSEs heavily; some only have minimum GCSE requirements. Some put a lot of emphasis on the UCAT; some do not. Some score predicted A-level grades, other don't consider them at all. You need to find the ones which you as an individual have the best profile for and apply to those tactically.
For b) you just need to look into the different locations, think about how you'd feel living there, look at where placements are (which are not always nearby but can be across the region!), as well as understand the differences in e.g. case based learning, problem based learning etc, and consider which you might prefer.
Also don't get too hung up on an individual specialty before you go to medical school - you'll still need to learn the full span of medicine in the degree, and then work across the range of medicine as a foundation doctor. For neurology specifically you also can only dual train neurology with internal medicine now so you will be working across the full range of medicine for 3 years in IMT, and then I understand will also have to do work in general internal medicine for the rest of your career. You will therefore have to be doing everything in "general" medicine for the rest of your career, as well as more specialised neurology work! You may also find at some point in the 10 years before you commence higher specialty training in neurology (5 years medical degree, 2 years foundation, 3 years IMT) that a different specialty appeals to you
