81 year old mum has lost her license and won't listen to reason. Any advice on what to say to her?

Beatty, who posts here has a lovely maxim "there will be no solutions as long as you are all the solutions". It is spot on.
You will need to set limits and boundaries with your mother. We are expected to do what we agree to do, and , more importantly, what we DO do.
It doesn't matter her regard or lack of for your "feelings". It matters what you say yes to. Tell your mother in a very nice manner that you will not be able to do these things for her. That she can get a place to live where she is taken care of, or avail herself of your offer to move more near, but that other options are out.
As to hoping she passes her license, when it is more than likely better that she no longer drive I will just tell you that it took my brother lying bleeding in the arms of his neighbor having smashed up his head, one palm tree and one refuse container to admit "I knew I shouldn't be driving; I knew something was wrong". Two months later, one month of rehab and one month of selling and moving to ALF, his life was quite changed.
Do let Mom know that you understand that she has problems, but that you do also, and that she should call you when she has good things to say, or the calls will be very short. Then see to it that you stick to it. There is no sense walking about with a "kick me" sign on post-its stuck to our forehead and then complain when the kick is delivered. You need to let people know what you will accept from them and what you will not. That is how life works.
This running out of a litre of milk thing often comes down to beginnings of fear, loneliness, neediness, because as we all know, it's easy to lean across the fence and say "Elmira, are you by any chance heading to the store today? I forgot my milk". Do know also that your Mom moving near you or worse yet in with you is not going to make anything even slightly better, but will be the beginning of an awful, likely decades long, slow slide downward. Reconsider that offer.
I sure wish you luck and hope you'll update us, but you will have to take this in hand before it gets quite OUT of hand.

Do not bring her to live with you. Being near may not be a good idea either if u want a life.

I am assuming ur from the UK. We have Office of Aging here that has senior bussing to appts and shopping. I would think England has stores that deliver groceries. Pharmacies that deliver meds. Mom is going to need to learn to use the resources at her disposal. Yes. set those boundries now.

You only need a few words, something like “I’m not doing that” or “call a car service” Your mother has confirmed that she’s not listening to reason so having long explanations won’t change a thing. And I wouldn’t keep encouraging the idea that she move closer to you or in your home, it’s an idea you’d likely regret

Once you know her strategy to get what she (thinks she) wants, you need to take control of the situation BY WAY of your, first: thinking, then secondly: your behavior.

* You need to ask yourself why you allow yourself to be entangled in this web - her web, when you have a daughter who needs her mother? Have you asked yourself Why?

* Why are you afraid of her / reactions to you, i.e., :
1. saying No.
2. saying you are busy now.
3. saying you need to make other arrangements, I cannot do this 'now.'
4. I'll let you know when I am returning. It might be (a) on Wednesday, in a few days, etc.
5. You'll need to ask ____ to help you this time. I am busy with my daughter right now.

If she doesn't have dementia, then she is repeating patterns of behavior in how she's interacted with you, likely for your lifetime. You need to go deep inside and ask why you allow her to control you and your behavior. So what if she's mad and having temper tantrums? She obviously will once you set boundaries. Does this frighten YOU to be on the receiving end of this behavior?

As I say "you teach others how to treat you" -

You must consider your own (quality of) life and that of your daughter, and, of course, your peace of mind and health . . . now and as time moves on. She certainly is not going to change. Whether she drives or not or wants a carton of milk or not, you need to regroup, take a few or many deep breaths and learn that it is OKAY, more than OKAY, for you to set boundaries with her requests / outbursts - whatever you want to call it.
Tough Love is Loving Kindness to Yourself.

After several dents were discovered on her car, I took my 89 year old mom's car to be serviced and didn't return it. She has the numbers for both local cab companies in her phone. They have her credit card on file. They take her to the store, library etc. I take food to her or have it delivered. Now that the weather is warmer and the hysteria has waned, I'll take her for a monthly shop... We both had mild cases of COVID in 2/2020 after I returned from a cruise.

Tell her to take a taxi or call uber, or offer to call for her. I say this all the time, but nobody can force you to do something you don't want to do. You are putting this burden on yourself. It's obvious she does not want to listen to your concerns, so you needn't listen to hers.

Daughterof1930: " And I wouldn’t keep encouraging the idea that she move closer to you or in your home, it’s an idea you’d likely regret."

Yes...THIS! Better get used to start setting boundaries NOW. If you have 2 sibs who are already uninvolved, your mother is going to look to YOU as she gets older and needs more help.

If there is a senior center anywhere in her area, they may have either a bus for shopping or a transportation service or volunteers. Check it out.

There is so much great advice here already. I’m repeatedly reading between the lines. You like your life. DO NOT HAVE MOM MOVE IN with you! Do not answer her every call. Be busy. Live your life. Be happy. Summer is coming with gardening and walks outdoors. Don’t allow anyone to make you feel guilty!

I would probably say the car is gone already and that would be the end of that.
Do not offer or let her move in with you. That would be a disaster.