The government's health reforms have been plunged into fresh doubt by a call from the Liberal Democrat peer Shirley Williams for Andrew Lansley to drop competition from the health bill – hours after the prime minister and his Lib Dem deputy defended the health secretary.

Writing in the Guardian, Lady Williams calls for the government to drop the chapter on competition, adding that the public has a fear of privatisation founded on the idea that GPs "might become dependent on advice from powerful private health companies, and that the imposition of UK and European competition laws, addressed to markets and not to social goals, might destroy the public service principles of the NHS".

"What is needed is willingness by the government, including the prime minister, to reach a compromise on the most contentious issues," Williams writes.

Her intervention, as leftwing Lib Dems mobilise to "kill the bill", echoes Labour's stance. With opposition mounting, the government has conceded more amendments. But Downing Street dismissed a call by the Lib Dem deputy leader, Simon Hughes, for Lansley to quit. The prime minister's spokesman said: "It's not an issue for Simon Hughes. The government is fully behind the health bill."

Hours later, Nick Clegg told the BBC: "Andrew Lansley is the architect of the NHS bill. He cares passionately about the NHS. He's the right man for the job and he must see it through."

Lansley broke silence to pen an article for the Health Service Journal in which he says competition will result in innovation. He compares health to music technology. "After all, in any other sector, it is the thousands of individual decisions to adopt a new technology – from, say, cassettes to CDs to MP3 players – which combine to sweep away less effective services."

Andy Burnham, the shadow health secretary, said the article reveals Lansley's agenda, for the NHS "to turn it from a national, collaborative health service into a competitive, market-based system."

In the House of Lords the government made, according to Labour, "major concessions" concerning the training of doctors. Ministers accepted an amendment which will force private providers of NHS services to give staff certain levels of training and education to avert fears that they could offer cheaper services by having less qualified workers.

The bill has suffered two defeats in the Lords and, in the light of such reversals, it appears that ministers are picking their fights more carefully.

Peers also questioned the role of the management consultancy firm McKinsey in helping to frame the bill following a report in the Mail on Sunday claiming that senior staff at the NHS body Monitor, whose role would include regulating healthcare contracts, had been "lavishly" entertained at the company's expense. Labour's Lady Royall said the company seemed "to be setting the rules in the health bill and benefiting from the outcome".

Earl Howe replied: "I know of no such impropriety. There are very strict rules … on declaring hospitality. If I discover any substance, I will write and place a copy in the library. I very much doubt that I will find any substance."

He added that between 2006 and 2010 McKinsey got £30m in work from the Labour government.