"I do not believe there are any bylaws whereby anyone can be taken to court"
Basically unless you have right of way or the permission of the landowner you're tresspassing. Right of way is easy to determine - look on an OS map. (NOTE: Though these are generally correct they do carry a little disclaimer that they may not be...)
If your intended route is marked as a footpath you have right of way on foot only (although you could legally walk a bike), if it's a bridlepath pedestrians, bikes and horses have right of way and so on for other types of right of way. If you have right of way then generally the landowner would need permission from the local authority to close it (although there are no doubt exceptional circumstances). A landowner could allow you further rights - they could have a cycle path on their land, for instance - if they so desire, and they could revoke those rights.
I *imagine* (IANAL) any prossecution for trespass would be mainly concerned with what you could reasonably think was allowed. I can't imagine you could (generally) claim you reasonably thought cycling was allowed in a pedestrianised area with no signs permitting it. However if, for instance, cycling had been permitted in the past or the signage was unclear (as it so often is) that may be a different matter...
There are also lots of other things that can affect right of way status and tresspassing, such as a history of usage and signage (hence signs on private industrial parks etc. that read "no right of way is granted by usage of this road" and so on).
So far as I can make out there are no rights of way on the South Bank, although there are a liberal spattering of blue cycle logos. I have no idea what those mean...
(IANAL = I am not a lawyer; therefore I wouldn't take any of my advice if I were you ;))
This post was edited by
10:38pm 8 April 2013.