I'm not sure what the query is.
The right to vote in England and Wales is based on having put your name on the electoral register, which in turn depends on nationality/immigration status and certain other statuses (eg not being a peer of the realm, traditionally). It's not related to liability to pay council tax as lots of people don't pay council tax, eg students, but still have a right to vote.
I don't know whether people with a severe learning disability are excluded from voting, but if they are it is only coincidentally related to any council tax exemption.
But of course, as often, there is a possibiity it is different in Scotland.
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