according to Wiki, Healey left the CP in 1939
But so did a lot of others who went "under cover" and cut all overt links with the Communist Party, but remained as secret members for years after
I have read (years ago) speculation that he was one of the purported "Oxford Spy Ring" the supposed undiscovered twin of the Cambridge ring but I don't think anyone has ever come up with any convincing evidence, let alone proof
However he was chums with Ted Heath, who did a pretty good job of wrecking the country, so maybe there is a ghost of truth in the theory...
Perhaps Healey, Heath and Thatcher were three of the Oxford four - after all the later two were both pretty destructive and arguably were partially the cause of the current collapse of the capitalist system (i.e Common Market, Banking deregulation....)