There are some secure car parks where you can park your bike. Some of them (for example, the one below the National Theatre) are free. Others, I think, offer reduced rates for bikes.
I couldn't find much specific stuff, but this:
http://www.westminster.gov.uk/services/transportandstreets/parking/wheretopark/vehicletype/motorcycle/carparks/
or this:
http://www.cityoflondon.gov.uk/Corporation/LGNL_Services/Transport_and_streets/Parking/motorcycles.htm
might be useful to you.
(Unless I could leave my scoot in a secure car park, I don't think I'd leave it hanging around St Pancras for a fortnight. But maybe I'm overcautious...)
Edited to add: parkingforbikes is also another good website. And they sell the EXCELLENT "cupcake" guide (a handy book with a map of zones 1-2 and all the bike bays, car parks, etc, marked on it. No connection to these guys, but I LOVE this book and would recommend it to anyone in London as an essential underseat item.)