I do not know if the prime minister authorised or knew about remarks made by his adviser Mark Britnell, who, at a recent conference in New York organised by the private equity company Apax, is reported to have said that the NHS was to become a "state insurance provider, not a state deliverer" of care, adding that this was "a big opportunity for those companies that can facilitate this process".

If Cameron did know about these remarks, this is a serious breach of faith with the British people, and with those of us in his coalition partners, the Liberal Democrats, who have been working hard on amendments to the health secretary Andrew Lansley's NHS plans. During and since last year's election, the prime minister has repeatedly refuted the charge that his party intends to privatise the NHS. If that is true, he must now dismiss Britnell from his "kitchen cabinet" and specifically reject his predictions for the future of the NHS.

The Lib Dems will not break faith with the British people, who have again and again declared their support for the NHS as a public service. Steve Field, the professor who chairs the NHS Future Forum, which is responsible for the listening exercise on the government's health proposals, has warned that the reforms could destabilise the NHS and destroy key services. The government now has to decide whether to drop the proposals or to alter them fundamentally.

There is, of course, a huge challenge facing the NHS – of having to make large savings while coping with an ageing population and the ongoing cost of the service's own success in saving the lives of seriously ill and injured people. The public understands that, and would accept changes in service configuration, for instance more care by GPs, experienced nurses and other health professionals, rather than expensive hospital care. In the last years of life, many patients who would once have died in hospital are now cared for by hospices, and that has been widely welcomed.

Lansley is right to press for such changes, and right to highlight the importance of preventive healthcare. But the integration of healthcare through closer co-operation between primary and secondary care can only be achieved in an NHS dedicated to partnership, rather than competition.

Lansley and his Lib Dem deputy Paul Burstow have agreed not to compel GPs to join clinical consortiums before they are ready, and to postpone target dates for this reorganisation. But their concessions do not yet address the core issues Lib Dems care aboutare devoted to and debated at their spring conference last March – issues that Field has emphasised: the NHS as a public service rather than as a market in healthcare. Here are some of the key changes Lib Dems would like to see.

First, the role of the secretary of state: as the excellent fifth report of the House of Commons health committee pointed out, the public, who pay for the NHS, look to the secretary of state to be responsible for the delivery of a comprehensive health service, one that is equitable, accessible to all, and free at the time of use. The National Commissioning Board will be accountable to the secretary of state; Monitor, the central regulatory agency that will license any new providers, should be accountable to him too, and should promote competition only on the basis of quality. Its main responsibility should be to promote integrated working and partnership between primary and secondary care and local authorities. The commissioning authorities should determine the shape of service provision, and should be able to commission services from a qualified provider if – and only if – that will complement the overall service provided.

Second, the original proposal for local commissioning bodies to be composed entirely of GPs has been heavily criticised. The Commons health committee, the Royal College of Physicians and the British Medical Association all suggest that the new consortiums should include specialist clinicians. There should also be representatives of other medical professions like nursing, of the local community and one or more independent members, including the chair. The consortiums should have a board, a chief executive and an identified finance director.

Third, openness: there is growing agreement that the local commissioning bodies must meet in public and keep records of their meetings that are open to public scrutiny. Members of commissioning bodies should register publicly any financial interest they may have. The current local authority scrutiny committees are valuable and should be retained.

Fourth, co-terminosity: as far as possible, NHS commissioning authorities should be co-terminous with local authority boundaries, to reduce complex bureaucracy, and to enable commissioners to co-operate with local authorities on social care, and with specialist networks for rare or chronic conditions. These networks are proving successful in improving quality while keeping down costs.

If amendments along these lines are adopted transition will be smoother, less expensive and less controversial. The same is true of the transition from NHS trusts to foundation trusts.

There is a high level of consensus among healthcare organisations and professional bodies about what changes are needed. If substantial changes are not made to Lansley's bill, the fallout for our party and for the coalition Government could be devastating, and could undermine the public's trust in us for years to come.