I guess chargebacks are less of a thing in the UK?
Fortunately I don't mind playing along and I'm pretty sure having this deliberately crazy process (instead of an online form) is a much bigger pain for my credit card provider (who are hoping for churn and people abandoning the process) than myself. Well, not me. It's not the £4, it's the principal.
This isn’t a complex calculus. Don’t do business with companies that steal from you, especially when they get upset that you took your money back.
Lyft in my experience has been pretty happy to give me my money back whenever I’ve had a problem. That’s the problem the OP ran into: Uber Eats didn’t just “mischarge” him, they refused to remedy the situation claiming impotence on their part. That’s what turns it from a “mischarge” into theft, and something a chargeback is both justified for and the correct remedy to resolve the situation.
My friends and I played outside in the front lawn of a house in "Mid-City" district of New Orleans and called taxi cabs all day as an experiment. Every 30 minutes we'd call another taxi to come pick us up. Not one taxi arrived all day. All of them claimed they came, honked in the driveway, but no one came out. Again -- we were outside the whole day, with full view of the street and driveway.
Also, a month earlier, the only taxi driver who once did drop me off there tried to illegally charge double until I called the police, who arrived after he left.
Uber/Lyft we had no trouble with at all!