The public want the health service to be free from day-to-day political meddling, according to a report from the body for NHS managers.
The wards cannot be completely free of politics, the body concedes
NHS leaders' and public views were converging, said the NHS Confederation, citing a poll in which 70% of 2,058 people asked rejected such involvement.
But it also suggested an independent NHS was unrealistic and undesirable.
Health Secretary Patricia Hewitt last week rejected calls to hand control of the NHS to an independent panel.
Prime Minister-in-waiting Gordon Brown has been reported to be in favour of asking such a board to run the health service on a day-to-day basis, in the same way that he gave up control of interest rates to the Bank of England in 1997.
Last month, the British Medical Association called for major change, putting forward plans for the establishment of a panel of governors and executive management board to run the NHS.
But in a report for its annual conference, the NHS Confederation said an independent panel was only "part of a solution", as it called for greater autonomy for local NHS organisations.
"Some form of political involvement is unavoidable in a service that spends over £100bn of public money," said its chief executive, Gill Morgan.
"The aim is to stop politicians interfering in the day-to-day running of the organisations which deliver and plan care."
According to a survey of NHS leaders, more than 90% agreed that better outcomes for patients were achieved when decisions were made at a local level.
But fewer than 8% felt that creating an independent board would facilitate this kind of decision-making.
"What NHS leaders want is genuine autonomy and accountability, with decisions being made as close to the place patients are treated as possible," said the confederation's head.
The Ipsos-Mori poll did not question the public on setting up such a panel, but seven out of 10 of the 2,058 people asked agreed that politicians should not be involved on a day-to-day basis.
Ms Hewitt has said that while the myth that ministers control every local decision persists, her department had "already taken significant steps towards creating an independent, self-improving NHS".
She has cited the creation of the National Institute for Clinical Excellence, the independent body which makes controversial decisions on which drugs to make available on the NHS, as an example.
In a speech last week, she stressed that more power should be devolved to patients, GPs and health staff.