Any question answered...

I'm driving down to Eastbourne tomorrow, early. If you can bear to get to Waterloo first thing then I can give you a lift to anywhere roughly between London and there- the bike will fit in the car without having to take it apart.
I cannot offer a lift back though I'm afraid.

Thanks for the offer. I'm taking the car so I can keep all my refills in it - I'll park it somewhere near the night circuit. I can always bail if I'm feeling too tired to ride.
I missed the rental place tonight anyway so will have to try again tomorrow. The logistics for simple things are always so complicated.