The most common local means of transport in British times was a two-wheeled cab for two to ride inside with driver mounted up behind.

One word substitute is Hansom.

Carriage: any of the separate sections of a train that carry passengers.
Wagon: a vehicle used for transporting goods or another specified purpose.
Locomotive: a powered railway vehicle used for pulling trains.
Hansom: a two-wheeled horse-drawn cab accommodating two inside, with the driver seated behind.