Health experts welcomed today's report but unions said the "NHS privatisation programme is still on track".
Chris Ham, chief executive of the King's Fund, said the recommendations would "significantly improve" the Health and Social Care Bill.
"The emphasis on integration is particularly significant and addresses a key weakness in the Government's original proposals.
"The 'pause' has served the NHS, its staff and patients well by allowing time to reflect on how to deliver the reforms the health system needs. But it is now time to move on.
"The Government must now move quickly to endorse today's report, put an end to the disagreements that have dominated recent months and provide the direction and stability the NHS desperately needs to navigate the challenging times ahead.
"Despite the headlines generated by the reforms, the key priority facing the NHS remains the need to find up to £20 billion in productivity improvements to maintain quality and avoid significant cuts in services.
"Implementing the reforms while maintaining the focus needed to achieve this will be very challenging and will require leadership and management of the highest quality throughout the NHS.'
Unite national officer for health, Rachael Maskell said the Bill should be scrapped.
She added: "The problem with Monitor is that it will now promote choice, competition and collaboration - all of which are contradictory aims.
"The hybrid mess that Monitor will become will do to the NHS what other botched regulatory bodies have done to other public services - from rail to social care.
"Unless patient care comes first, then Monitor will fail patients - and our politicians will have failed them too."
She added: ""The way that David Cameron and Health Secretary Andrew Lansley will interpret the Future Forum's recommendations is that the pace of the privatisation of the NHS will be slowed down, but not abandoned - that's the crux."
Dave Prentis, general secretary of Unison, said: "Really big questions over critical issues such as privatisation remain unanswered: just how will the Government prevent "cherry-picking"?
"And why are there no limits on the amount and range of services that can be privatised?
"The Forum is recommending sweeping changes to the Bill because it is riddled with flaws.
"It exposes the real agenda behind the Government's Bill - the wholesale marketisation of the NHS.
"It wants to turn our health service into nothing more than a logo on the side of a van run by a multinational company."
Dr Peter Carter, chief executive of the Royal College of Nursing (RCN), said: "We are pleased that the NHS Future Forum has used the 'pause' period to listen and reflect on the concerns that the public and professionals have over the future of the NHS.
"We welcome the report's findings that Monitor must support the integration of care and that care must not become of secondary importance to cost.
"Equally, we fully support the report's conclusions regarding the importance of transparency within the new commissioning consortia as well as the recommendation that private firms must not be allowed to 'cherry pick' services.
"However, it is disappointing that the Future Forum appears not to have accepted the view of thousands of our members, who are calling for a mandatory requirement for nurses to sit on the board of every commissioning consortia."
The Royal College of Physicians' president, Sir Richard Thompson, said: "We urge the Government to grasp the opportunity to give hospital doctors a mandated place on the board of local commissioning bodies to guarantee integration of primary and secondary care.
"To encourage this, the RCP also wants GPs to sit on the boards of foundation trusts. In this way all doctors will work together to lead a health service in the best interests of patients.
"The recommendation that Monitor's role should be altered from promoting competition to promoting collaboration and integration is a step in the right direction. The Health and Social Care Bill must clearly state that the primary focus of regulation is promoting integration, collaboration and quality - not promoting competition."
Dr Jennifer Dixon, director of the Nuffield Trust, said: "On balance, the report forms a good basis for taking the Bill forward.
"There will be a temptation among some to prolong the debate in the hope of further concessions but the time has come to amend the Bill, and move on.
"Political focus needs to shift urgently to the difficult decisions confronting the NHS.
"Further uncertainty would likely have a demoralising effect on clinicians and managers, and make the already difficult job of achieving unprecedented efficiency savings even harder."
Professor Peter Furness, president of the Royal College of Pathologists, said: "Market forces only work if the buyer can measure the quality of the product.
"GP leaders have confirmed our view that GPs cannot be expected to assess the quality of diagnostic services beyond their speed and price, so we welcome the requirement for multi-professional commissioning.
"But we wait to see how this will be implemented. There must be appropriate multi-professional input that has 'clout'.
"We fear that commercial companies will offer only commoner diagnostic tests, thus destabilising the NHS provision of tests for rare disorders and limiting the availability of specialist advice. It's good to hear that 'cherry-picking' will be prohibited. But how? Will it work?"
Mike Farrar, chief executive of the NHS Confederation, said: "This report makes big strides in the right direction and has a real chance of getting NHS reform on the right path.
"The Forum has run an exemplary process and we are delighted that it has taken the lion's share of our recommendations on board.
"It suggests clarity about who is accountable for what, as opposed to confusion for patients and the public.
"It suggests an intelligent approach to integration and competition, not a one-size-fits-all system that risks fragmenting services.
"It suggests a realistic timetable for transition, not a rushed approach that risks some parts of the NHS losing control of finances.
"We are now calling on the Government and Parliament to deliver such changes and urgently provide the NHS with the legislative framework needed to make these ideas workable in practice."
Dr Hamish Meldrum, head of the British Medical Association (BMA), said: "The way the Government and the Future Forum have engaged with the profession during this listening exercise has been a refreshing experience. It is vital that this constructive approach is maintained in the following months as the detail is worked on.
"The Future Forum's recommendations address many of the BMA's key concerns, to a greater or lesser extent.
"We are hopeful that our 'missing' concerns, such as the excessive power of the NHS Commissioning Board over consortia and the so called 'quality premium' will be addressed as more detail emerges.
"While we welcome the acknowledgement that the education and training reforms need much more thinking through, there needs to be immediate action to prevent the imminent implosion of deaneries.
"Obviously, the critical factor is now how the Government responds, as well as ensuring that the detail of the changes matches up to expectations.
"But if the Government does accept the recommendations we have heard today we will be seeing, at the least, a dramatically different Health and Social Care Bill and one that would get us onto a much better track."
Dr Clare Gerada, chair of the Royal College of GPs, said: "We are reassured that things are moving in the right direction; the emphasis on preserving the principles of the NHS and keeping it free at the point of need; freeing the NHS from political interference; clinical commissioning of local services led by GPs; and the real focus on reducing health inequalities are to be welcomed.
"We are encouraged by the Forum's recommendations for the future role of Monitor in relation to competition, and the report's insistence that private providers should not be allowed to 'cherry pick' patients.
"But we still have a number of outstanding concerns about the potential risks and unexpected consequences of the proposals.
"We need the Government to reassure us that GPs will be given the freedom and autonomy to lead the decision-making and design of future integrated health systems drawing on the support of other health, social care and third sector services.
"We support clinician-led commissioning but continue to believe that GPs are best placed to lead this process."
TUC general secretary, Brendan Barber, said: "This report sets out to reassure those who have been so critical of the Health and Social Care Bill and of the immense changes it is seeking to bring to the NHS.
"But whilst well-meaning, any attempt to bring clarity to what started out as a fundamentally flawed Bill was always going to be difficult. We are still left with a dog's dinner of a Bill.
"Downplaying competition in Monitor's remit is all well and good in theory, but the unenviable task of attempting to balance this with choice and collaboration in practice is still likely to mean that it is patients, particularly the most vulnerable, who will end up losing out."
Susan Anderson, CBI director of public services, said: "The healthcare system is in urgent need of reform and the Health and Social Care Bill is crucial to ensuring the NHS is well placed to meet the challenges of the future.
"These include an ageing population and greater demand from patients with long-term and chronic conditions.
"The report rightly recognises that the best way of delivering the high-quality services that the public expects is by allowing a diverse mix of qualified providers to deliver services, including from the private, voluntary and third sectors.
"Greater competition should also go hand in hand with further integration of services to ensure they better meet the needs of individual patients."