Mode S transponders can relay additional information, including the permanent identity of the aircraft
As far as I am aware, UK ATC are not going to get the software which would enable the Mode S 24-bit code to be translated to the tail number.
Currently (I was told by NATS at West Drayton on a recent visit) the tail number appears next to the radar blip only if the plane is on an IFR/airways flight plan, in which case the tail number is looked up from the squawk and from the flight plan which pops up on the computer. There won't be any immediate way for ATC to get the tail number of some VFR (or IFR OCAS) traffic that is simply flying around.
Does seem rather stupid - the tail number would be rather handy when trying to contact somebody