As parent said, the USA market is unique. How do you know your taxi has suitable insurance! Or insurance at all? Insurance laws in China are completely different from the US (everyone is seriously under insured, even the normal taxis).
I have no idea about England. Not everyone lives in England, some of us even live in Asia. My point is that Uber should follow the laws of the countries they are in, and if those laws are holy (in the sense that adequate insurance is not enforced or not apparent), then that is a problem with the laws, not Uber's business model.
How would I know the driver has an insurance which covers driving people for profit? The usual insurances do not. If something would going to happen to a passenger they do not know whether that is covered.
Well that seems to be a problem with legislation not the uber model per se. Just don't see the problem but then again I don't live in the UK so I don't hear about all those examples of that happening.
The legislation is already there: If you drive around you need insurance. That is a sensible policy. Uber saves cost because neither they nor their drivers are appropriately insured. It's only a matter of time until something bad happens.
It's not a problem of legislation but a problem with Uber.