The other thing the UK has is the small claims court. Many large companies have insurance terms that mean that they have to be represented by competent lawyers,

The other thing the UK has is the small claims court. Many large companies have insurance terms that mean that they have to be represented by competent lawyers, and unlike other tracks in civil law costs are not recoverable in the small claims track. So large companies often don't have any option but to lose money if you start to take them to court -- either spend a lot of money on lawyers, which is sunk forever, settle out of court, or don't show up and pay the bill when the order comes from the judge. If I were in the OP's position I'd report Uber to trading standards, threaten to take them to court, and quite possibly follow through with it, representing myself. They're an odious company and have quite clearly just nicked money here with no recompense.