The BP petrol station here is closed and every other garage has queues on to the road.
I'll admit I did think I'd get petrol when I was out today. I have half a tank and I do generally keep it topped up for emergencies, although I would probably have left it until next week to fill up normally.
In the event, I didn't bother queuing but I'm guessing most of the people "panicking' are just filling up a few days earlier than they usually would. After all, a tank only holds so much, it's not as if you can buy a year's supply like toilet rolls