At a guess, someone chucked a cigarette end over the hedge into my front garden and set fire to the cover, which spread the flames to the plastic parts of the bike - looks like I've lost both mirrors, the windscreen, the rear number plate, and damage to the seat and luggage, but nothing really fundamental to the actual functioning of the bike has been damaged.
So I've spent most of the intervening time contacting the police, insurers, etc. What ought to happen next is that I talk to the insurers again tomorrow and arrange to have the bike collected for repairs, and probably spend a week or two travelling by public transport while it's sorted.
To say that I'm not a happy bunny is putting it mildly, but nobody has been injured and it looks like it's repairable. Things could be a lot worse.