Neurological physiotherapist

No. You’ll get a band 5 job in the nhs and you’ll do rotations most probably through the more common areas of physio such as resp, neuro which you want, msk, surgery and so on. These will be 4-6 months in duration depending on the trust and ordinarily you’ll be at it for a couple of years before considering a band 6 job, though nowadays all bets are off and people are progressing quicker. As a band 6 you’ll do the same as a band 5 but the rotations will be 8 months or so in length each. Some trusts will have specific neuro only ‘cogs’ so you can stay in neuro and do things specific to that, but with many you’ll again be rotating through general areas.
At band 7 level this is generally when you’ll specialise and remain static in an area. You won’t need any additional training at all, though by now you may well have done some masters modules or other training such as bobath. Neuro is usually a competitive field with jobs highly sought after, especially at large neuro rehab centres. As a general comment, undertaking additional study isn’t going to set you apart from others at the more junior levels, and indeed is a total waste of time for band 5 and band 6 levels. I’d question the point at 7 too. Get your nhs job and get churning patients. Even if you are 100% certain you’re going to be a neuro physio now you may discover another interest when you get going. The other point is that you’ll need skills in other areas to be a more complete therapist. Got a stroke patient with a subluxed shoulder? Ok, no problem I did an MSK outpatients rotation as a junior so I know how to tape it and strengthen the rotator cuff. Got an MS patient with a weak cough? Ok no problem, I did respiratory as a junior so I know how to invasively suction and use the nippy airway clearance. Got a patient with cognitive issues? Ok, I know how to do a cognitive assessment due to working with older adults. Do not specialise too quickly!