Remove the speedometer from the car.
Take a nail or rod and file a square profile on its tip so it fits the square hole in the back of the speedometer. Chuck the re-shaped nail in an electric drill and set the drill to run in reverse (counterclockwise). Hold the re-shaped nail to the drive hole in the speedometer and run the drill slowly. If the needle and odometer move, the problem is the cable to gauge connection. If it doesn't you are looking at speedometer repair.
Also check the top end of the speedometer cable core while the gauge is out. Early cables were typically ground "square" to fit the speedometer. Later cables are often swaged to form an oval instead. The oval doesn't always fit the speedometer's drive hole well. Examine the cable end carefully if the speedometer appears to be working properly with the drill.
Speedometers can be repaired but I have no idea how much it costs in the U.K. Contact Speedy Cables and ask for a general guideline for what you can expect to pay.