It's a 1939 Rover 14 Drophead Coupé, a car that was produced from 1933 to 1940, and then again from 1945 to 1948. This 1939 model had a 6-cylinder 1901cc engine. The brochure of the event had this to say about the car:
1939 Rover 14 Drophead Coupé
This model was produced in small numbers by Salmons and Son, coachbuilders, in 1939 and 1940 using the Rover Sports Saloon as the basis.
This example was supplied from new to Northern Ireland. It returned to the UK in 1991 and has since been restored, having been off the road for several years. "Dizzy" as she is affectionately known, has just returned from her first continental trip to join in the celebrations of the 10th anniversary of the Belgian Rover Club.