Bad luck about County Hall being full.
What is making you feel so nervous, harman? Is it the appointments, or travelling, or london?
If you're good at walking, it is a fab Tahmes path walk (of no more than a mile, I think...) between Tower bridge and St Thomas's, and passes Borough market, the Golden Hinde, the Clink, The Globe, Tate Modern and 'wobbly bridge', Coin St with it's little shops and playground, and the South Bank.
There is a PremierTravelInn at Borough market / london bridge.
Try Laterooms.com?
Is it next week?
I am chokker next wek and then away, but I bet some London MN-ers would meet you at lunch or in the eveninhg or for tea if you put out a shout!