Taxi drivers are exempt from wearing seatbelts while seeking hire, answering calls for hire, or carrying a passenger for hire. If they aren't working they should be wearing one (i.e. using the car for personal purposes).
The reasons for this rule are a bit vague, ranging from getting away from assaults to spending large amounts of time getting in and out, but the fact is, they are exempt.
The difference between Hackny Carage and Private hire is:
Hackney Carage Taxis are able to pick up fairs off the street. They can be 'waved down' and can take unbooked fairs. They exist all over the country, but only in big cities do they tend to be the London Cab style cars. If you have ever gotten into a Taxi anywhere without having to book, it was a Hackney Carage. It is a different licence governed by the council, with tests done on cars suitability annually aswell as driver health checks and other rules. Its more difficult to get a Hackney licence. It is classed as Public Transport (pensioners can use their travel tokens in Hackney Cariges)
Private Hire Taxis can only collect pre booked fairs. You are not able to 'flag down' a private hire taxi. They can only collect booked work. They cannot pick up from taxi ranks. They arent as strictly regulated and I dont think the cars are tested, and im not sure even the drivers are. Easier licence to get. They are a hireable private service. Just like a Limo. They are Private transport (i.e. no Pensioner travel tokens)
A hackney carage driver can be exempt from wearing a seatbelt all the time at work as they will always be deemed to be 'seeking' a fair whenever not carrying one as they can be flagged down at any time. Private hire cars are not working while not carrying a fair, so are only excempt whilst carrying a fair, as while not carryign a fair they are not seeking, they are simply another road user.
Make sence?