My Westwood T1600 won't start?

My mower won't start using the key.
The ignition light comes on in the first position, but nothing happens when I turn the ignition key to "start".
I can start the engine by shorting out the solenoid (screwdriver blade across the two terminals).
I have replaced the ignition switch and the solenoid, which hasn't solved the problem.
It must be down to wiring / connections?