Apart from residents parking, the only paid motorbike parking I've seen is in Westminster, where you have to call up a number to pay as soon as you park your bike. Something like £1.50/day. I guess it all gets done by cameras there.
Don't know how it is with Southwark, have a look at the council website (sorry I would look but it's too late)
http://www.southwark.gov.uk/YourServices/transport/parking/
If you can't find any thing, then aren't the motorbike bays still free?