What are the rules about take a bike on the London Tube?
Transport for London page on Bikes on Public Transport

On the tube, folding bikes are good anywhere at any time.  Non-folders are restricted to only certain lines - in most cases these are lines that have no deep below ground tracks - and certain times. 

To a certain extent it is going to be up to the station/train staff.  I've travelled on the DLR with my bike in the past, before I realised they have a total ban (I was dismissed from the train, which sucked because I'd had a few to drink and was trying to avoid cycling home).  If in any doubt, or trying to wing it, its always worth asking before you enter the station.