Labour has written to the top civil servant at the Cabinet Office over alleged briefing from Downing Street against Andrew Lansley, including a claim that a No.10 staffer said the health secretary should be "taken out and shot".

In a letter to Sir Jeremy Heywood, Labour's Shadow Minister for the Cabinet Office Jon Trickett asks whether there'll be an investigaton into the anonymous briefing.

"Will you now launch an investigation into how a Downing Street source could make similarly tasteless remarks about a member of the Cabinet?" writes Trickett in his letter, published by Labour.

A column by the Times columnist Rachel Sylvester on Tuesday claimed (£) an unnamed "Downing Street source" said Mr Lansley "should be taken out and shot", and that Downing Street was seriously considering giving the Blairite former health secretary Alan Milburn a peerage, so he could replace Lansley at the Department of Health.

Later on Tuesday morning a No.10 spokeswoman insisted Lansley continued to enjoy David Cameron's "full support", despite mounting criticisms of his planned NHS reforms and press speculation about his future in the Cabinet.

Asked about the reports on Tuesday morning, a Downing Street spokeswoman said: "The Prime Minister backs Andrew Lansley and he backs the reforms we are pushing through Parliament in order to deliver a better health service for the future."

The spokeswoman said she "did not recognise" reports of Mr Milburn's name being floated as a possible replacement for the Health Secretary.

Mr Lansley's Health and Social Care Bill is expected to face a rough ride from peers when it returns to the House of Lords tomorrow, less than a week after the Royal College of GPs wrote to Mr Cameron calling for it to be scrapped.

Labour leader Ed Miliband is also urging the Prime Minster to dump the Bill, warning that opponents of the legislation have just "three months to save the NHS"

Shadow Health Secretary Andy Burnham said on Tuesday afternoon: ""A campaign is clearly underway to scapegoat Andrew Lansley. But it is David Cameron who has put the NHS on a knife edge and it can't afford to have a lame-duck Secretary of State in charge who does not have authority and the personal support of the Prime Minister.

"Rather than looking for someone else to blame, he must now take responsibility for breaking his personal promises to NHS staff."

Today, two leading lights in the pro-reform NHS Alliance and National Association of Primary Care warned of flaws in the design of the planned changes.

Dr Charles Alessi and Dr Michael Dixon told The Guardian they were concerned that new GP-led clinical commissioning groups will find themselves under the control of a National Commissioning Board, in place of the Primary Care Trusts and Strategic Health Authorities which are being abolished to grant frontline workers more autonomy.

They warned that the proposed new structure involves "layers of bureaucracy and management with complex guidelines".

The fact that many of the NCB's staff are likely to come from the old PCTs and SHAs "adds to clinical commissioners' concerns and perceptions that they will be suffocated instead of liberated, which in our view is fundamental to the success of clinically-led commissioning", they said.

Dr Alessi told The Guardian: "What we are hearing and seeing are the same old messages and the same old structures, albeit with new nomenclatures.

"If we put the same ingredients into the mix, the likelihood is that we shall deliver the same inefficient environment and outcomes. This is insupportable in an economy of tight financial restraint."

The Downing Street spokeswoman said: "As far as we are concerned, the reforms are going to deliver a better NHS, one which will be freer of bureaucracy and have less political interference. It will mean that health care workers can get on with delivering care to patients.

"We have made our position very clear about what the reforms we are legislating for will do to improve the NHS and put the powers and decision-making ability into GPs' hands."

Asked whether the PM was concerned about the scale of opposition from bodies including the British Medical Association, the Royal College of Nursing and leading healthcare journals, the spokeswoman said: "Understandably, lots of people have different views on our reforms, we accept that.

"We are very clear that they will deliver an NHS which is freer of bureaucracy. The fact is that we have to reform the NHS.

"As the population gets older, we can't continue to put money into the NHS in a similar sort of way. It has to be reformed.

"We believe that putting the NHS in the hands of the health professionals, rather than a bunch of bureaucrats is the way forward."

The spokeswoman denied reports, attributed to former No 10 aide James O'Shaughnessy, that last year's "pause" in the legislative process to consult with health professionals was merely a "tactic" to ensure the eventual passage of the bill.

Mr Cameron had made clear that the delay would give ministers an opportunity to "listen and reflect", and this had resulted in amendments to their plans, she said.

"While the fundamental reason for reform hasn't changed, we have paused, we have listened and we have improved the bill," said the spokeswoman.