What are the regulations surrounding bus lanes and why are some vehicles allowed to use them, but no

Bus lanes have been a bone of contention with many drivers, ever since the first bus lane was marked out and came into operation.
The world's first designated bus lane to be marked out was in Chicago, Illinois in 1940, while the first bus lanes to be established in Europe were located in Hamburg, Germany in 1963.
It wasn't long before other German cities followed on from Hamburg’s example, and in 1970 the implementation of bus lanes was officially sanctioned in the German highway code.
The UK finally followed suit, and on 26 February 1968 a bus lane was created and brought into service on Vauxhall Bridge, London.
Since 1968 the bus lane network in London has grown and there are now in-excess of 150 miles of bus lane in London sevicing 6,500 buses, with many hundreds of miles servicing the rest of the UK.
With the advent of ViaVan and other on-demand services, confusion seems to have arisen as to which vehicles can actually use bus lanes.
According to Transport for London the following can all use bus lanes in the capital:
buses which have a minimum of 10 seats, including the driver
licensed London taxis
motorcycles without side cars
mopeds
scooters and tricycles which are non-motorised, motorised under 450kg and not with side cars
bicycles
Private hire vehicles as well as all other traffic are prohibited fron entering bus lanes.
In some cases a sign may display the word 'local' indicating that only local bus services can use the bus lane.
These rules differ across the UK, for example, although a London or Birmingham bus may be defined by the requirement of having 10 seats, in Manchester the requirement is that a vehicle must have 9 seats to be defined as a bus.
What needs to be remembered is that it doesn't matter what a company name is, if a vehicle has the permissible number of seats to enter a bus lane, then it doesn't matter whether the vehicle is operated by ViaVan, UberBus or Fred Bloggs Coaches, they can enter a bus lane, and be afforded the same rights as any other bus company.
Image Source: Geograph
Image Author: David Dixon