YANBU to feel upset. Now the question is - are you going to do anything about it?
I think this is quite indicative of the type of person he is - "he might as well have got an Uber as I was supposed to be saving him money by giving him a lift". Did you know you were supposed to be saving him money? I expect you thought you were being helpful (you were), but he saw your help in purely financial terms.
And then, at the checkout - "He said loudly where other people could hear" - so not just stingy, but actively trying to humiliate you. This is designed to stop you ever asking him for anything ever again, because the risk of humiliation will feel too great. It's quite a controlling behaviour for him to deploy.
"... and I just said I would transfer him the four pound but he wouldn't accept that and then said it had been a joke."
No, it wasn't a joke. You know it, I know it, he knows it. It's an attempt to pull you back onboard. Don't fall for it, because things are NOT going to go back to how they were. If you stay in this relationship, he would now know that he can treat you like this, humiliate you in public - and you'll put up with it. So he'll do it more. He'll do it even more humiliatingly. He will escalate - they always do.
"I feel so humiliated and upset and I'm seriously considering dumping him as surely this is likely to just be the start of his meanness?"
Do dump him - it's your best choice. It's not just his meanness, it's his whole attitude, the being a user, the willingness to humiliate you. And this is not the start of it, it's always been there. What this is the start of, is him letting his mask slip and testing your boundaries. He's seeing how much bad behaviour on his part you will accept. That's why it's important to accept nothing.
Bin, bin, bin.