This is the Dunkley Pramotor, introduced in 1921, or 1923 according to some sources. The Pramotor was a scooter attached to the rear of a large baby pram, and the intrepid nanny rode standing astride the engine on the scooter platform. Early versions were powered by a 1 HP horizontal single-speed two-stroke engine.
It was manufactured by W.H. Dunkley of Birmingham, UK.
There is more info here.
This is clearly a genuine 5-wheeled vehicle, in the 4+1 format. They are rare but you can see some in the N-wheel car gallery of the Museum.
Ooh-er, is that a golliwog in the pram?