The NHS guidance states anyone with a chronic neurological condition should be offered the flu vaccine for free. 

The guidance indicates that your GP should assess to take into account the risk of flu making any underlying illness worse, as well as risk of serious illness from flu itself. Any infection makes ataxia worse, therefore most GP's will not have an issue with this. However, if your GP rejects this, you can ask your neurologist to write a letter.

The vaccine should be free for everyone who is at risk, and should be offered for free for people who live with someone who's at high risk of coronavirus (live with someone on the NHS shielded patient list / or you expect to be with them on most days over winter). Click here for more information.