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.