The Sun welcomes the further easing of lockdown restrictions - saying that after "10 gruelling weeks, at last there's good news for millions of Brits longing to see their loved ones".
But its opinion column urges readers not to let the "new freedoms" go to their heads - saying they must do everything in their power to avoid a second wave of Covid-19 cases.
The Daily Telegraph similarly welcomes Boris Johnson's announcement, but it calls on the government to take a "more nuanced" approach to social distancing.
The paper suggests that making people stay 2m apart could be counter-productive, particularly for some businesses. The answer, it thinks, may be to allow "reasonable adjustments" - if, for example, ventilation is adequate, or people are wearing masks.
Readers of the Daily Mirror are told that some dentists may be wearing gas masks when they start to reopen their doors on 8 June. A dentist in Greater Manchester tells the paper that medical-grade face masks are so hard to obtain that some practices are buying gas masks from DIY stores online.
On its website, the Economist asks why Britain and the US have not followed the lead of other countries and made it mandatory for people to wear face masks in public. "That is regrettable," it says, because "masks could both save lives and allow people to get back to work".
It accepts that in normal circumstances a government might hold out for better scientific evidence in favour of masks but concludes that "these are not normal times".
The Daily Mail claims Dominic Cummings is considering leaving his job as Boris Johnson's most senior adviser later this year.
But it suggests his possible departure has nothing to do with the row about his trip to County Durham during the lockdown. The Mail says it's been told by "well-placed sources" that Mr Cummings wants to be in the post to see out his two main aims: cutting the UK's ties with the EU, and shaking up the civil service. But once those are achieved, he could resign.
On its front page, the Guardian reports that health officials proposed what it describes as "a radical lockdown of care homes" to curb coronavirus deaths. The strategy, it says, was submitted last month by Public Health England.
But the Guardian says it was rejected by the government. The Department of Health responded by saying it's working tirelessly with the care sector to reduce transmission and save lives - and all decisions are based on the latest scientific and clinical advice.
Finally, the Times proclaims that the "Bright Young Things are back". The paper says a century after the jazz-age hedonism captured by Cecil Beaton's photographs, there's a resurgence of interest in the scene.
An exhibition of his work at the National Portrait Gallery in London had to close because of the pandemic.
But its curator predicts that as the lockdown eases, "young people are going to let themselves go in a way that the Bright Young Things did, after the restrictions of the First World War".