I can remember that 'procedure' on the Lightning often having unhappy consequences, and I am sure BOAC can too. The closed down engine would invariably windmill, and the engine-driven fuel pumps would try to pump the non-existent fuel that had now been shut off by the HP cock. The result was often a clattering loss of integrity of the fuel system, with large fuel leaks resulting when the HP cock was re-opened and the engine re-lit for the rendezvous with the tanker or the recovery to base.
Given the proximity of pooled leaked fuel and hot bits in the Lightning, the result was all too often a Martin-Baker let-down, a paddle in the North Sea and the welcome appearance of a bright yellow helicopter.
So, idle all you like, but shut-down I'd rather you didn't.