It won't be. Speed limits have been imposed under various local measures over the years, including in Royal Parks and along certain parts of the Thames Path. They tended not to be enforced as there was no reliable way of determining the cyclists' speeds and speed cameras and speed guns at the time had not been approved for evidencing speeds below 30 mph. Most of the speed restrictions on cycles have been rescinded.
However, a number of speed guns have now been approved for evidencing speeds of 20 mph+, which may be why Southwark are thinking of introducing a limit. Southwark has something of a schizophrenic relationship with cyclists - on one hand it claims to encourage and with the other it seems to do everything it can to make life difficult (e.g. the proposed ban on cycling on the Thames Path they mooted a few years ago). Hopefully Jenny Jones will get this plan kicked into the long grass, the same as she has done with their other stupid ideas...