Southern site showing Bognor to London services running normally. And the £17.30 price should apply on all the trains - less 50% if you find yourself with three friends. And you can't reserve a bike space on Southern.
Righty. I think the lack of reservations (which seems to be a recent development, I've certainly made them in the past) was causing the system to fail non-gracefully with "there are no trains, the end of the world must be nigh" messages.
On that basis, I've booked a 2pm train out of Euston, and will endeavour to make it back to London in good time by groupsave improv. Can't be arsed with the Clapham Variation, as I tend to lack the sense of humour required for all the hanging around involved when sleep-deprived.
(As for riding back to London, my fitness is way down, as demonstrated by having a thoroughly miserable time with 100k of rain and headwind last weekend. On that basis, I'm off to get some miles in...)