My first full summer spent in England (in Cambridgeshire) was summer of '03 - heatwave summer!!
How well I remember! I had flown over to see my [then] boyfriend [now husband]. Had been to London twice before and - forgive me, but I'm one of those weirdos - LOVED the gray, overcast, cool, rainy weather. (Always have.) Coming from the Southern US with its abundant heat, humidity and sunshine - and AIR CONDITIONING - I was so, so, so uncomfortable!
But, you know, this thread about hot/cold, etc.: everyone's personal thermostat is so different (I know mine is!) that I'd have difficulty recommending what clothes to bring/leave behind.