Okay. Op has said she doesn’t want to pay the delivery charge. £5 doesn’t sound much to most of us. We don’t know her finances.
We also don’t know about how she’s feeling, her MH etc. Perhaps the car failing it’s MOT and the looming costs have really thrown her. Perhaps she doesn’t cope well. Some people in life need favours or ask for favours from friends, that seem intrusive or too large and unreasonable to many of us.
However, it’s all about context isn’t it.
We don’t know the exact context. I suspect that all is not rosy if OP is asking her friend to do this driving and take this time, rather than get a delivery. There’s probably more going on than just wanting to get a load of shopping.
I’d also suggest that many in this thread seem very harsh and to struggle with the concept of putting yourself out for someone. Of course, it’s totally fine that the friend said she couldn’t take OP shopping. Someone doesn’t have to give a favour and often there can be good reasons not to and it’s fine to say ‘no’. But equally, it’s fine and good to say ‘yes’ too - even if OP could have spent £5 on delivery. Even if it will cost money and take up valuable time. Being a bit self-sacrificing is what lots of people do for their friends when they seem in need, and even for people they don’t really know. Perhaps that’s an alien concept to some people.
The thing is, someone doesn’t have to be desperate and have zero alternative options for someone to ask for help, and those asked should feel they can consider saying yes, and that they’re not being taken huge advantage of, by saying yes, to anything which is less than a desperate plea. It’s a mindset - to either be generous or stingy in our willingness to help others.
Again, it’s fine that the friend said no. But if she had said yes and incurred the cost of petroleum and loss of a couple of hours, that wouldn’t have made her a mug, or OP a CF for asking.
Most of us wouldn’t have responded to the situation by asking the friend to give the lift. Most of us would have organised a delivery or got a taxi or gone to a local shop. The fact OP didn’t do these things, possibly tells us something about her situation not being quite usual and her needing more support than might be initially obvious. I think it’s hard for people to imagine that too, or to not have a reaction of shying away from it, or thinking it’s simply an outrageous ask.