Chainless bicycles were popular in America, where they were supplied by a variety of manufacturers, with Columbia the leading exponent. France’s leading brand was Metropole. The Belgian FN chainless was also very well constructed, and Durkopp copied that system to produce their own chainless gear for the German market.
Quadrant made a chainless bicycle in Britain in the 1890s and though it sold reasonably well, the great advances in cycle technology around the turn of the century meant there was a lot of competition from cheaper and simpler chain-driven bicycles. With European and American demand for chainless bicycles already well served, there was no opportunity for British exports of a chainless gear. So there was little incentive for British manufacturers to build one.
When Components Ltd took over Rover Cycle Co in 1912, one of their first innovations was to strike a deal with Durkopp to provide a chainless gear for the Rover. It was introduced to the British market in 1913 as the Chainless Rover Roadster. Unfortunately we will never know how the British cycling public would have taken to it in the longterm. War broke out between Britain and Germany a year later and trade ended between them, so the Rover Chainless was only in production for one year.