General Stanley McChrystal's indiscreet discourtesy towards President Barack Obama in a Rolling Stone magazine profile was no accident. The article was not an excuse for his sacking; it was more the parting gesture of a military leader who recognised the irreconcilable when he saw it. It was the symptom of diverging approaches. We should make no mistake: the replacement of Gen McChrystal by David Petraeus is the beginning, the very beginning, of the end of the international coalition's presence in Afghanistan, although it will not be admitted for a while.

Mr Obama had agreed, with utmost reluctance, and after long and rather impressive deliberation, to Gen McChrystal's strategy of a military surge creating the conditions that would allow a quick exit. But it has been clear for some months that Gen McChrystal's strategy required more time than the President was willing to give it. The Independent on Sunday also reveals today why the President thought that the strategy is not working. We report that the US military's own assessments express profound concerns over the state of the campaign, worsening security in coalition-held provinces, and corruption in the Afghan government, army and police force. These are precisely the issues that this newspaper, which was the first (and is still the only one) to call for British troops to be withdrawn on a phased timetable, has been emphasising for some time.

Those are powerful indicators that point in the wrong direction, and the President was entitled to demand evidence of the effectiveness of US spending, currently running at $7bn a month. Plainly, Mr Obama was not convinced that Gen McChrystal's strategy would turn things round quickly enough. Indeed, it seems to have been the General's resistance to the President's demand that US troops start to pull out next year that made his indiscretion unforgivable.

The tide has turned in Afghanistan, then. It was interesting that David Cameron was the first leading British politician to sense the moment. The Prime Minister, in his statement to the House of Commons on his return from Afghanistan two weeks ago, made clear that British strategy would be determined by political rather than military imperatives. In other words, that war is too important to leave to the generals.

This weekend, he repeated that our troops "can't be there for another five years". This was not a timetable – perish the thought – but it was a welcome shift in the direction of realism. British casualties in Helmand have been rising, with increasingly little to show in the wider picture. Mr Cameron's change of tone was one that fitted perfectly with Mr Obama's shifting view, despite an initial media reaction that assumed another split between Britain and America, mirroring the genuine tensions in the special relationship over economic policy. That shift was reflected in the words that emerged from the G20 meeting yesterday.

With surprising speed, the international coalition seems to be coming to the position that we set out on Remembrance Sunday last year. A political settlement with those elements of the Afghan Taliban that are negotiable. A recalibration of our ambition in Afghanistan from reconstructing the entire country to containing its capacity to act as a base for jihadist movements. Continuing development aid where provably effective and corruption-free. (As we report today, the economic potential of the country's minerals reserves is beginning to be reappraised by the mining industry; but that wealth can be realised only if there is a political settlement.) The military effort limited to training Afghan forces, protecting development projects, policing the Pakistan border and special forces. The rest of our forces to be brought home on a phased timetable.

Gen McChrystal's departure is preparation for the time when such a new strategy could be espoused openly by our political leaders, on both sides of the Atlantic. As Patrick Cockburn writes today, the skill of his replacement, Gen Petraeus, is to use his reputation as a military tactician to conceal political manoeuvres. He can use his image as the man who turned the tide in Iraq to take the credit for a new approach in Afghanistan.

Whoever takes the credit for it, and however much our leaders insist that the new strategy is merely a continuation of the old, what matters is that the international community sets itself realistic and realisable goals in Afghanistan, and that we end the loss of our troops' lives as soon as possible.