Recently, after a good downpour of heavy rain, when I turn the ignition I get the 'bulb out' light and buzzer come on. No bulbs are blown and once the car dries out a bit it starts fine without any warning.

It's not a massive issue, I may have a search round the bulbs next time it's been raining heavily, but just posting to see: Is this crazy voodoo, or has anyone else had something similar?

Make sure the plenum chamber drain holes are clear and clean out any debris. Water can build up in there if it's all blocked up. The water than damages the main wiring loom, and it gets VERY expensive to repair.

At the risk of revealing my utter incompetence; what's a plenum chamber?

I think it's the bit between the top of the bonnet and the bottom of the windscreen. Leaves and other junk can get collected there. Sure someone will correct me if I'm wrong.

As Haniball says, it's the channel between windscreen and bulkhead. Good luck getting the wiper arms off

Just use a wiper arm puller, just the tool designed for the job. Will lop em off in minutes without damage.