Regency England teemed with carriages, especially during the daily promenade through Hyde Park. The carriage pictured here is a landaulet, a small version of a landau.
A landau was a four-wheeled carriage with two passenger seats facing each other. The two-sectioned roof could be folded down or left up depending on the weather.
The landaulet was just a smaller version of that with one seat and a retractable roof. The one pictured here was featured in Ackermann's Repository in March 1819 for the moveable axles it has.
*Ackermann's Repository, 1819, page 125