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I am well qualified to write this answer because it has been an established family task for me to drive my mother or father everywhere if they ask, for so many years, ever since I became a competent driver in 2003. Here in India it is a son's duty to drive his mother wherever she wants to go (but not a daughter's duty) so the cultural background is very relevant to this question.

Even in UK where you live, an Asian or Middle Eastern family may have different cultural expectations in this matter compared to a native British family, because in many Asian cultures (and other "traditional" societies) parents have the moral right to demand anything of their offspring, simply because of their massive contribution to making us what we are, though you can decide how true that is in your particular case.

The ideal interpersonal approach, if you have good and frank channels of communication with your mother, and especially if she is a reasonable and fair-minded person, is simply to tell her (when she is relaxed, and after you drove her somewhere, not before) that it is costing you money you can ill-afford and request her to suggest some solution. That puts the ball in her court and she can decide how she would like to compensate you for your expense, or what alternative she might select instead.

Things to be careful of, if you can have that duscussion:

  1. Make sure your mother is in a frame of mind to positively take this discussion.

  2. Be sure not to put her on the defensive by accusing her of wasting your time or money. You should avoid any negative-sounding statements.

  3. Emphasise that you are glad to help her by driving her anywhere but it is costing you, and that is why she finds you saving less money.

  4. So how can you help me to help you, Mother?

If having such a clear discussion is not possible in your family then one remaining option is to assert yourself by driving her most times when she demands but sometimes avoiding it with whatever excuses you think will work in the short term. That demonstrates your general willingness to drive her around while asserting that you are your own person and she cannot take your availability or co-operation for granted. So she will have to be prepared with an alternative means of transport for that occasional situation, pay for it, and also, hopefully, begin to think about the cost of your driving her substantial distances for free.

The best thing to do after asserting yourself is to work out a system of recurrent reciprocal favors that will take your mother where she wants to go and make your time and expense worthwhile. For example, one of my young student friend age 20 routinely drives his father to work at a mobile phone company and reciprocally Father often gets him substantial employee-incentive discounts for data plans, freebies, etc. It could be anything... Maybe your parents could sponsor the next repair your car needs, or pick up the tab for your next educational expenditure? That's how my parents 'recognize' my services as a driver.

That sort of thing keeps the balance in the interaction and reminds your parents that you are now an adult willing to do them a useful chore to be reciprocated with certain benefits, rather than the obedient child of not-so-distant memory. Meanwhile you can consider that you are substantially working off your "unrepayable debt of gratitude to your parents", from the Asian perspective.