Leaning the perennial catchphrase of Professor C.E.M. Joad, 'It all depends what you mean by'
The COP will have to be involved with any loan.
If your mother has ~£100k and, allowing for care fees, ~£5k can be loaned to you for 1 year, and you pay interest (best for 1 yr deposit I know of at the moment is 1.85%), and you can prove that, in addition to repayments, you can afford insurance and other running costs, and you can show that use of the car will be primarily (but not exclusively) in your mother's benefit you might have a slim chance of the COP agreeing.
Additionally it will all have to be set up legally (which may cost), not forgetting that your mother's interest will be included in her income for tax purposes.
Coming down to reality, there is an argument that reasonable transport costs, depending on circumstances maybe taxis, to visit your mother could be in her best interests. As you have an EPA, rather than a deputyship, you don't have to produce accounts. You have to be accountable for any expenses if anybody starts an investigation as to where the money has gone.