The CAA says yes!
I've revived this thread as I have an answer from John Brady of the LAA on CAA 'policy' on voluntary fitment of transponders
"the CAA have confirmed you can fit an A/C transponder without restriction as long as you don't try to fly in airspace where mode S is mandatory (Airways and IFR in the London TMA). "
So much of the official output is almost misleading. Given the present low cost of Mode C units it would be well worth getting hold of one and fitting it!