The Hackney Horse
The Hackney Horse isn't the most common of British breeds; it and the Hackney Pony are now on the Rare Breed Survival Trust's Endangered list, which means there are between 300-500 adult breeding mares left. The Hackney, like the even more endangered Cleveland Bay, has presumably lost popularity as carriage driving became a sport rather than a mode of transport. Here's some film of when there were rather more of them about.
The Hackney Horse was descended from the Norfolk Trotter (amongst other breeds), which figures large in K M Peyton's historical duo, Small Gains and Greater Gains. If you want to understand the fascination trotting races held, her books are an excellent place to start.
and from the 1920s: Princess Mary presents prizes at the National Hackney Show in Doncaster
NATIONAL HACKNEY SHOW