Criticising the lack of vision for the under-pressure health system, the Bishop of Carlisle, the Rt Rev James Newcome, said the value of such an agency was "blindingly obvious" and described the response by the administration as "deeply disappointing".
The creation of an Office for Health and Care Sustainability, likened to the fiscal watchdog the Office for Budget Responsibility, had been a key recommendation of a Lords select committee on the long-term sustainability of the NHS and adult social care.
In its conclusions, the committee highlighted a "culture of short-termism" in the NHS and adult social care.
Criticising the "short-sightedness" of successive governments, the inquiry found almost everyone involved in the health service and social care system seemed "absorbed by the day-to-day struggles, leaving the future to 'take care of itself'".
The committee said a new political consensus on the future of the health and care system was "desperately needed".
Speaking during the Lords debate on the report, the bishop, who sat on the committee, stressed the need for a long-term view.
He told peers: "We need to be looking at 15 or even 20 years ahead and at present that is simply not happening."
The Government had dismissed the suggestion of an independent body arguing it would "replicate existing mechanisms", but he said: "Existing mechanisms are not currently prompting or helping anyone to plan for the long-term sustainability of the NHS and adult social care.
"I believe that this dismissal of our fundamental recommendation is both perfunctory and inadequate."
Opening the debate, committee chairman Lord Patel, a former consultant obstetrician, believed a "real celebration" to mark the upcoming 70th anniversary of the NHS would be "a political consensus".
Calling on the Government to take the lead, he said: "The Prime Minister's legacy would then be the delivery not just of Brexit but, importantly, sustainable health and social care.
He added: "The time has come for a political consensus to make our much-loved NHS a service that delivers the best care for all, is cost-effective and becomes the model of the best care in the world.
"It is doable, as long as the NHS does not continue to be a political football for those who hope to win votes."
But opposition health spokesman Lord Hunt of Kings Heath cautioned "about the desire to create a cross-party approach".
Warning that decisions on health and social care "cannot be offshored", he added: "In the end, you need a Government with the political will to make the investment necessary, put in place a plan to fix staffing and properly support people to manage their own health care and conditions for the long term.
"Labour did it. We increased the amount of money going into the health service, reduced waiting times dramatically and invested in the infrastructure. It can be done, but it takes a Government with the political will to do it."
However, his rejection of the need for a consensus led to criticism from Liberal Democrat peer Lord Willis of Knaresborough, who said: "Simply talking about the problems we have today, without being able to look ahead to 10 or 15 years, which is exactly what the report does, does a disservice to this House and the whole of the NHS and adult social care."
Tory former health minister Lord Prior of Brampton, who was part of a review that found the annual cost of the NHS would rise by £50 billion by 2030, argued the need for a long-term settlement so that people in the NHS could plan for the future.
He said: "If we look back over the life of the NHS, there is a correlation between the amount of money going in and the productivity that is coming out of the NHS.
"One Government comes in and puts too much money in, and productivity goes down.
"The last Labour Government... got the NHS to make huge progress, but during much of that time in the early 2000s a lot of waste and inefficiency went along with that extra money going into the system."
Lord Prior added: "We need a long-term settlement so that people in the NHS can plan for the future. It is not hard to create a long-term settlement, because the spending on the NHS is so determined by demography and technology that it is quite easy to predict."
Independent crossbencher Baroness Murphy said a minimum 20-year plan was needed for the NHS and added: "My question is not how do we sustain the current system but why do we want to given its sad state."
Lady Murphy, who worked in the NHS all her working life as a doctor, a psychiatrist and then a manager, said the situation was "far worse" than people believed.
"I am ashamed now when I compare the health care here in England to what is available in other European countries," she said.
"In particular the primary care system of which we were so proud is now so poor in delivering access to people that we are the fourth worst (European country) in having people unable to access (health care) and ending up in A&E instead."
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