IO540, I don't know the specifics, but if your at 35nm range from Shawbury's radar, you blip size may well be quite large if various filters etc are not switched on. I would certainly expect an aircraft with reasonable radar cross-section to appear to be at least 2nm across in azimuth. Combine that with a radar map which, although accurate, still has 'line thickness', a keen, puppy controller and you may well find that he/she believes you are about to commit a mortal sin.
Can't comment on Lyneham, sounds like ATC supervisor bull**** to me.