It was the mixer shower as you suggested. I put the shower temperature on full-cold only and turned it on, then turned on a nearby mains cold tap and the shower pressure immediately dropped (I've since traced the pipework to confirm).
A final proof was that by leaving the mixer shower in the...
PEDANTICVINDICTIVEMAN - I may be a bit late on this, being as the original post was in June but is there a simple test for the mixer-tap problem?
My loft tank that feeds the HW cylinder is also overflowing in the same way. If I sit and watch it I can see the wavy shadows of the hot water...