Any question answered...

Don't know if it's the Cable Cafe ed refers to, but there's a new cafe on Brixton Rd by the bus-stops closest to Oval tube, which is really nice and has a couple of small cafe tables outside on the pavement, not really ideal for sitting with bike but ok.

Them's the badger.

Also Brunswick House 5 minutes walk from Vauxhall Station is a great cafe to leave your bike outside while having a lovely cuppa and pastry,