In January 1945, when victory in Europe had become inevitable, Winston Churchill received a private letter from Clement Attlee, the Deputy Prime Minister, deploring, in civilised and well-reasoned prose, the manner in which the Prime Minister increasingly did things in his own arrogant and eccentric way without recourse to the War Cabinet. Furious at first, Churchill had to eat humble pie, if only because most of those around him agreed with Attlee. Good leaders learn to adapt.

A bit of humble pie for Kevin Pietersen and Peter Moores is required if the ridiculous mess in the England cricket team is to be cleared up before mud sticks to everyone. Neither should lose his job, given some clear thinking and plain speaking. Neither, in fact, has much of a record: England have won seven Tests out of 22 under Moores's guidance as head coach, only one of these against a top-notch team, and that consolation victory in the last Test against South Africa in August had much to do with Pietersen's batting and captaincy.

The new captain, however, has swiftly had to learn that a flurry of one-day victories over a South Africa team content with the main prize in the bag, was delusory. The Stanford embarrassment and India's excellence in November and December put things into clearer perspective.

Pietersen conducts himself exceptionally well in public and he showed initiative and decisiveness in bringing back Stephen Harmison, then dropping him when he was not satisfied with his response, not to mention in leading the full team back to India after the terrorist horrors in Mumbai. But his team were thrashed in the one-day series in India and if he thinks that Michael Vaughan would have been the difference between a fine victory and the actual honourable defeat in the Test “series”, he is probably mistaken.

Times Archive, 1974: Boycott walks out

To an uncommon degree, Boycott is a man driven by personal ambition. This being so he finds it more difficult than most to accept a subordinate position

• Times Archive: Sport

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The selectors were right not to imagine that Vaughan would be the immediate solution to England's repeated failure to find a reliable No 3. Ian Bell has scored no hundred in that position after 29 innings and Owais Shah has been given only two Tests in the role, in the first of which, in India on the previous tour in 2006, he was a great success. Vaughan himself, although it is a perfectly feasible argument that the captaincy was scrambling his brain, has failed to adapt his game as all very talented batsmen must. I would have brought back Robert Key as Andrew Strauss's opening partner and dropped Alastair Cook to No 3.

Pietersen had every right, naturally, to express his preference, but an independent selection committee usually works better than a captain/coach cabal, even when they are in agreement, always provided that the selectors normally give the captain the team he wants. The decision over Vaughan was tricky. Geoff Miller, the national selector, has to stand or fall by it.

It remains questionable, with a batting, bowling, fielding and spin-bowling coach in the mix already, plus Phil Neale as the operations manager, whether England need a head coach. India managed rather well without one between the departure of Greg Chappell and the arrival of Gary Kirsten. The whole England system is top-heavy with chiefs, but that is another argument.

In practice, the best cricket teams are run by a strong captain, not a strong coach, so Moores will have to accept that if the new captain wants more rest and recreation time, and perhaps more practice rather than physical training, that is the way it should be. There would be no disgrace in a compromise from which captain and coach emerge with their roles more clearly understood. In Moores's case that means being more a skilled facilitator, which he is, less a man-manager, in which skill he had his failures even in his time as coach at Sussex.

But Moores is a passionately conscientious man and John Buchanan proved in his often shadowy role as Australia's coach “under” the captaincy of Steve Waugh and Ricky Ponting that relationships can work even when the captain knows that there is nothing his “coach” can teach him about batting.

Pietersen, like most of the England batsmen of the time, enjoyed working with Duncan Fletcher more than he does with Moores, but if the captain has truly offered only a “me or him” ultimatum, Hugh Morris, the England managing director, surely has to back the coach, who was promoted on the strength of rising to the top of the carefully graded coaching system that Morris set up for the ECB. To replace Moores, for example, with Graham Ford, who played seven first-class matches and has merely South Africanised Kent, would be ludicrous.

The inconvenient recommendations of the Schofield report after England's pathetic performance in Australia two years ago (such as a leaner domestic structure) may duly have been ignored by the ECB, but at least it took the advice to have an accountable England managing director. So, Morris has to take a decision that his two subordinates accept. He has to make it clear to Moores and Pietersen that neither is as important as the England cricket team that they are both extremely well paid to represent.