I still can't see it. Pretty much every single minister has leapt to his defense - if they punt him now, it'll look bad on them. The only way I can see out of it is if Cummings resigns but still doesn't admit defeat and states that he's resigning to allow the govt to focus on the real issues instead of being harassed with nonsense or some such patter that will be a ridiculous attempt to save face. Even then, I can't see Cummings doing that - He seems the type that'd rather bring them all down with him.
Therefore, deny, deny, deny seems to be the logical (And embarrassing) option.