<<they sometimes have to drop into LVPs coz they are sitting in cloud while everyone at ground level can see quite clearly!.>>
Been in that situation many, many times at Heathrow.. Maybe it doesn't happen too much now with the cleaner air.
The original surface radar - ASMI - at Heathrow was not a daylight viewing radar so the tube had a large hood attached to it to shield it from the light. Controllers often became so engrossed in doing GMC "under the hood" that when we eventually took our reddened eyes out we'd find it was CAVOK. Did our colleagues tell us? No way Jose!!! Great times....