With regards to John Prescott, I agree with the PM that their roles are somewhat intertwined, but there is a way out!
In 1968 the Labour Deputy Leader, George Brown, quit the cabinet. However he remained Deputy Leader until 1970 when he lost his seat. In 1976, Deputy Leader, Edward Short quit the cabinet when Callaghan became PM (The two apparently disliked each other), but remained Deputy Leader until that autumn, when he quit as MP.
I know that the rules say that, in government, the Leader and his Deputy have to be in the cabinet, but apparently there is a loophole somewhere, and if it is true, as most Labour supporting newspapers state, as do a range of Labour MP's, that Prescott's presence in cabinet is a liability, then (and I say this reluctantly) he should do the decent thing (but perhaps remain Deputy Leader) or face the consequences, and no one wants that, apart from the Conservatives and Liberal Democrats, and loyalty is not a word that has always been in their vocabulary.