I'm not sure weather the controllers base their height for infringements on primary contacts or the Alt mode return, but I'm guessing the xpndr return.
Primary radar, unless you've got very sophisticated, military-style multi-lobe radar, doesn't give any altitude information, just lateral information (position).
The altitude is solely based on mode-C returns. No mode-C, no altitude, simple. And I believe in the UK any aircraft squawking mode A only, is assumed to be below the base of whatever controlled airspace is concerned.
All airborne Mode C encodings are always referenced to 1013. SSR altitude information must be referenced to the same datum to ensure correct TCAS operation.
True. That's why you will never have to put the altimeter setting in your transponder. The datum is always 1013.2.
However the controller has the ability to enter the local QNH (or QFE I suppose) into the radar scope so that he can watch the altitude (or height) of aircraft that operate below the Transition Layer.