Hi Will,
If your mother is in receipt of Guarenteed Pension Credit, or Universal Credit, she will be entitled to claim taxi fares to and from her hospital appts. Your mother must get a form signed from her Consultant, or the check-in clerk. A receipt from the taxi driver is essential. Then your mother can claim her fare back in full. There is a payment office in each hospital who deals with this. Proof of her entitlement is required, either by post or on the day.
Hope this helps! If your mother is unable to walk to the office desk with all her proof, you may have to step in and send these documents by post for her.