Thanks for the super-prompt reply.
I've just checked, when I tried your test I thought I saw the FI light flicker very briefly, so I cycled the kill switch, it came on for a split second longer. I cycled it quite a few more times and then the fuel pump came on - so I'm presuming the kill switch is suffering from corrosion or worn?
After the fuel pump stopped priming, I tried the starter and the engine cranked over (yipee ;-) ), but didn't start. I pulled the 'choke' out and tried again, but nothing. It cranks but doesn't seem to fire at all.