Labour leader Ed Miliband is calling on the public to join a three-month campaign to kill off the government's controversial NHS reforms as pressure mounts on David Cameron to withdraw the coalition's flagship health and social care bill from parliament.

Ahead of a crucial week for the health secretary, Andrew Lansley, during which the bill will return to the Lords where it can expect a further mauling, Miliband describes the plans as a dangerous "leap in the dark" that will impose a "free market free-for-all" on the NHS.

With much of the medical profession now opposed to the plans and Downing Street increasingly concerned, Miliband says an effective cross-party campaign in parliament, backed by patients, could deliver Lansley's plans the last rites.

"It is not too late to stop this bill," Miliband says in an article for the Observer. "We have three months to prevent great harm being done to the NHS. Now is the time for people of all parties and of none, the professions, the patients and now peers in the House of Lords to work together to try to stop this bill." The worst option, he argues, would be to press on with a bill just so that the government can save face.

Ominously for the government, Labour, Liberal Democrat and crossbench peers are discussing joint strategies to torpedo further elements of the bill when it begins its report stage in the Lords on Wednesday.

The latest action to amend the bill – which would devolve power over commissioning to GPs and open the service up to more competition – comes despite the government offering a string of concessions when it put down 136 amendments in addition to the 1,800 already tabled. One peer involved in cross-party discussions said the aim was to continue amending the bill until ministers had to concede there was no further point in pressing ahead.

Labour and some Lib Dem peers, including Shirley Williams, are now training their sights on the part of the bill that would open the NHS to a greater role for the private sector. "This is the core of the bill," said one peer. "This is what really matters." Labour and the Lib Dems, with some crossbench support, are tabling further changes which they say will limit the extent to which the private sector can compete to provide services across the NHS.

Peers predict the government could suffer a series of defeats between now and March. Privately, many Tory MPs question whether it is wise to press ahead with a bill not backed by most of the medical profession.

Last week, physiotherapist leaders joined the Royal College of GPs in calling for the health bill in England to be scrapped, becoming the latest medical group to set its face against the plans.

Changes agreed by ministers last week, intended to win peers round, include making it clear the health secretary would retain ultimate control over the NHS, and strengthening the requirement of the regulator, Monitor, to ensure different providers competing for patients also work together.

But there are signs that peers are going for more concessions. The Observer understands that some prominent Tory peers may soon break cover to voice concerns about key elements of the bill relating to its provisions on competition.

Miliband is keen to stress his party is not against all reform. "The NHS needs reform, but not David Cameron's. A sign of a reform being on the right track is whether it slowly builds support, as the Labour government did with the tough action we took to get waiting times down, including using the private sector where appropriate."

Defending the reforms, Lansley said: "The NHS faces unprecedented challenges from our ageing population and new, more expensive treatments.

"Our plans to improve the NHS are essential if it is to be sustainable for the future. Doctors and nurses support the core principles – giving more power to clinicians to design services for patients, getting patients the information they need to make proper choices and promoting democratic accountability, with councils leading health improvement. Any reform of something as important as the NHS will cause controversy.

"Trade unions like the BMA opposed the very creation of the NHS. Labour used to support reform but now they are jumping on the bandwagon of opposition in order to please their trade union masters. My father worked for the NHS on the first day it came into existence, I want the NHS to still be here to support my children in the future. I care passionately about maintaining an NHS that is free for all which is why I am pursuing a programme of reform to make it sustainable for future generations," he said.