Andrew Grice: While the PM and his deputy jockey for credit, Labour is the real winner

Downing Street insists that the NHS Future Forum, which proposed big changes to the Government's health reforms yesterday, is an independent panel which reached its own conclusions.

If that is right, it's just a happy coincidence that David Cameron foreshadowed the most important changes in a speech a week ago and Nick Clegg has been discussing them in detail with his MPs for a couple of weeks.

It suited both the Prime Minister and his deputy to involve an independent body to help them convince health professionals and the public, who take their cue from the professionals, the Government was genuinely listening during the unprecedented "pause" to the Health and Social Care Bill.

This U-turn is the most important of the several now completed by Mr Cameron – health is a toxic issue for any party, particularly his own. Contrary to claims by bruised Tory MPs, Mr Cameron's main motive has not been to toss sweeties at the Liberal Democrats because they were routed at last month's elections. The Cameroons have been spooked by polls suggesting the Tories are in danger of losing their hard-won trust on health.

The choreography of the U-turn has not been easy. Mr Cameron and Mr Clegg wanted the same outcome and agreed a pincer movement against Andrew Lansley, the Health Secretary and architect of the reforms – who, to his credit, admits he did not think through the political consequences. He is the biggest loser.

Yet there have also been real tensions between the Prime Minister and his deputy since both wanted to reap a political reward from the "reforms to the reforms". They have jockeyed for position in recent weeks to try to keep their own nose in front in the credit stakes. After Mr Cameron's pre-emptive strike in last week's speech, Mr Clegg declared victory over the weekend, leaving the Tories seething.

Although it is true that the Liberal Democrats demanded sweeping changes to the Bill at their spring conference in March, their dismal showing in last month's elections highlighted the need for them to show voters they enjoy real influence inside the Coalition. That meant shouting victory on the NHS from the rooftops. "If we don't tell people about it, no one else will," one Lib Dem aide said.

Yesterday, Mr Cameron and Mr Clegg reassured their own MPs that they – not the other guy – had called the shots. Today, they are likely to end hostilities as they try to rally their parties behind the revised policy.

But the amended Bill may well not necessarily cure the Coalition parties' ills. The voters will not follow the fine print about the role of the NHS Commissioning Board. But they will know that the Government tinkered with their NHS, possibly at its peril. Although Mr Cameron has pledged inflation-plus rises, the NHS budget will virtually flatline and the £20bn of efficiency savings needed over the next four years will mean an unprecedented cash squeeze.

The danger is that when patients notice the consequences, they will blame the Coalition's reforms rather than the need to cut the public deficit (widely seen as Labour's fault). So health could be a big issue at the next general election. Despite yesterday's proposals, the party that would stand to benefit most would be Labour.