Let us not forget that Denis Healey, as Minister of Defence, was a former member of the Communist Party. Was he PV'd?
While on my joined-up writing course at Bracknell many decades back, the general topic of security clearances for Ministers was raised in questions from the floor to the then SoS for Defence. The response was twofold; first part along the lines of "how dare you cast aspersions against government ministers"; second part was "impossible, it takes far too long."