Boris Johnson has been urged to start holding daily coronavirus press briefings as criticism of the UK government’s media handling of the crisis grows.

All three Labour leadership candidates demanded greater clarity, and Nicola Sturgeon, Scotland’s first minister, also spoke out as her officials sought to clarify a warning from Matt Hancock, the health secretary, about the over-70s having to self-isolate at home for up to four months.

The opposition parties have largely been supportive of the government’s handling of the coronavirus outbreak, but there have been at least three incidents of Whitehall giving out contradictory messages, with the uncertainty compounded by the fact that some key reporting has been based on unattributable sources.

Keir Starmer, the Labour leadership race frontrunner, said that over the last 48 hours ministers had been “failing in their responsibilities to provide consistent and transparent public health advice” and that allowing the public to learn about significant changes in policy through anonymous briefings was “irresponsible”.

“It’s time the government commits to a daily press conference about its handling of coronavirus. This must be hosted by a government minister or the prime minister himself, with experts and advisers available to answer questions as appropriate,” Starmer said.

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Rebecca Long-Bailey also called for daily briefings to be broadcast, and Lisa Nandy said the government had to publish much better information because the last 48 hours had been “a real shambles”.

Nandy singled out as an example Sir Patrick Vallance, the government’s chief scientific adviser, giving an interview on Friday morning defending the decision not to ban large sporting events only for No 10 to brief that evening that a ban would soon be implemented.

In his interview, Vallance also spoke about the potential advantage of the UK acquiring some element of “herd immunity” to coronavirus, echoing an argument used by another adviser and the head of government’s behavioural insights team, Dr David Halpern, earlier in the week.

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Vallance’s comments triggered a fierce backlash on social media, with people claiming it amounted to evidence that the government was happy for large numbers of people to get coronavirus. On Sunday, Hancock had to distance himself from Vallance, saying “herd immunity is not our goal or policy”.

The health secretary then found himself being contradicted by officials in Scotland. He said the government would soon ask the over-70s to “stay self-isolated” at home for four months, but his use of the term “self-isolate” was taken by some to mean the elderly would be told not just to minimise contact with others, but to avoid it altogether.

Catherine Calderwood, Scotland’s chief medical officer, told the BBC that what was being proposed for elderly people was “reducing social contact, rather than self-isolating” and that it was “scaremongering” to suggest they would be told to sit “home alone”.

When Jason Leitch, the Scottish government’s national clinical director, posted a message on Twitter making the same point, Sturgeon commended him for providing “important clarity”.

Sturgeon went on to add in another tweet: “Giving clear and consistent information to public at the right time on coronavirus is vital. Governments’ media strategies must reflect the importance of that.”