A leading Liberal Democrat sparked renewed speculation about Andrew Lansley's future when he said David Cameron should find a new health secretary after the health bill becomes law.

The Lib Dem deputy leader, Simon Hughes, said he believed Lansley needed to "move on" in the second half of this parliament so the government could put the controversy over NHS reform behind it.

Hughes's comments will not be welcome in Downing Street, where Cameron has been defending Lansley in response to calls from the influential ConservativeHome website for him to be replaced and an anonymous briefing from a No 10 source saying Lansley should be "taken out and shot".

Hughes spoke out as the Labour party stepped up its attack on the health reforms by releasing an internal Department of Health letter saying that "too many patients" are facing unacceptable delays because trusts are failing to meet their waiting time targets.

Speaking on the BBC's Andrew Marr show, Hughes said: "I'm clear we need to move on from this bill." He went on: "My political judgement is that in the second half of Parliament it would be better [for Lansley] to move on."

When pressed as to whether he was saying that Lansley needed to be replaced, he confirmed that he was, although he also accepted that he needed to be "careful about the political sensitivities of this coalition".

Lib Dem ministers are expected to defend their coalition partners in government. Although Hughes is not a minister, he is the most senior figure in the party to call for Lansley to be replaced.

In an article for the Mail on Sunday, the Conservative MP Nadine Dorries claimed that last week's anonymous Number 10 briefing against Lansley must have been authorised by Cameron or George Osborne. "I fear the malicious briefings will continue and Lansley will be replaced as soon as Cameron and Clegg can agree upon a replacement ready to please the Lib Dems," she said.

A YouGov poll for the Sunday Times shows that only 18% of people say they support the government's NHS reforms. Another 48% oppose them, with 34% saying they are not sure.

In an article in the Sunday Times, Cameron offered fresh support to his health secretary. Arguing that the NHS needs to change, Cameron said: "That is why I am at one with Andrew Lansley, the reform programme and the legislation going through parliament."

Cameron also insisted that the changes in the health bill were "evolutionary, not revolutionary".

On Sunday Conservative cabinet colleagues offered Lansley their support. "Andrew is very committed to the health service," Eric Pickles told Sky. Pickles said that "of course" Lansley should stay and that, as communities secretary, he was "very supportive" of the bill "particularly as it enhances the role of local government".

Jeremy Hunt, the culture secretary who has been tipped as a possible successor to Lansley, told the Andrew Marr show: "Andrew Lansley is absolutely the right person for this job. [He] is a decent man, passionate about the NHS and he knows what he is doing."

On Sunday Labour released a copy of a letter sent to all NHS chief executives on 2 February from David Flory, the deputy NHS chief executive, in which he says that in some areas waiting times are unacceptable.

"In November 2011, 47 commissioners and 30 acute trusts failed to meet the 90 per cent admitted standard," Flory wrote referring to the rule that 90% of patients should be seen within 18 weeks. "Performance in some treatment functions also needs to improve – most notably in Trauma and orthopaedics where the largest numbers of patients continue to wait longer than 18 weeks."

The letter goes on: "Waiting times are a key part of patients' perceptions of the NHS and their care and can impact on patient outcomes. It is unacceptable for performance to fall below the expected standards."

Andy Burnham, the shadow health secretary, said the letter showed that standards in the NHS were already getting worse.

"This confirms what Labour and health professionals have been telling David Cameron all along: the government is damaging frontline patient care with its distracting top-down reorganisation of the NHS," he said. "More people have waited longer than 18 weeks for their operations, one-year waits have gone up by almost 200 per cent and major A&E units have missed David Cameron's lowered four-hour target for the last six weeks in a row.

"With long waits up since the election and nurses being cut, David Cameron should listen to Labour, drop the bill and use the money saved to protect 6,000 nursing posts that are set to be cut by this Tory-led government."

Government sources accept that peers, who restart voting on the health bill on Monday, will inflict a series of defeats on the legislation, and ministers will have to concede more to rebels in order to get the bill on the statute book by the end of the parliamentary session in April.

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