Thanks for that mk1escort2build - I tested the switch using the continuity function on my multimeter (continuity to ground), and I found out that holding the gear lever over to the passenger side makes the circuit, and leaving it alone or pushing it to the driver's side broke the circuit. I'm thinking of just picking up another switch and swapping it over and seeing if that works.
The only other thing I thought could be wrong is that the gear lever is quite 'sloppy' - there's a reasonable bit of play once a gear is selected. Does anyone know if maybe the selectors need adjusting? I thought that if they do it could be exacerbating the problem with the switch.
Forgive me if this is an obvious thing to do, I haven't had a lot to do with gearbox work!!