A neighbour claims they spotted Mr Cummings dancing to Abba with his family in the garden, saying: "I looked over the fence and got the shock of my life. I was really annoyed."
A number of opposition MPs tell the Guardian the Downing Street aide should lose his job.
But a source close to Mr Cummings says there is "zero chance" he will resign.
Elsewhere, employers will have to pay a quarter of the wages of furloughed staff from August, according to the Times.
The paper says that under government plans to unwind the scheme, to be announced by the chancellor next week, firms will be required to make the payments even if they are still in lockdown.
A Treasury source tells the paper that with two full months of support left, it is fair to everyone that businesses contribute as people return to work.
The Daily Telegraph reports that Boris Johnson is planning to scale back the role of the Chinese technology giant, Huawei, in the UK's 5G network, reducing it to zero by 2023.
A source tells the paper the deal was struck before the pandemic - and that coronavirus had "changed everything".
The Guardian thinks this is a retreat by the prime minister, designed to stave off what could have been an embarrassing defeat in the Commons.
The Daily Mail leads on government measures it says could allow families to holiday abroad this summer.
Ministers are reportedly aiming to strike quarantine-free pacts with destinations such as France, Spain and Greece, by as early as July. They are also said to be considering so-called "Covid passports", which would allow someone who has had the virus to travel more widely, and not have to go into quarantine on their return.
The Sun also sees reason to be optimistic about a summer break, urging it's readers to "jet your hopes up".
The Financial Times says that with millions stuck at home, many families are reviving long-held dreams of having a pet to accompany them on socially-distanced walks.
This, the paper says, has resulted in a puppy shortage, with many breeders reporting a surge in demand, leading to soaring prices and long waiting lists.
But charities tell the FT they are already seeing examples of dogs being handed back as people return to work. Buyers are urged to remember that a dog is for life, not just for lockdown.
And the Sun reveals details of a novel plan under consideration by several Premier League football clubs, that it is hoped will improve the atmosphere in stadiums when matches re-start.
Cardboard cut-outs, filling the seats, featuring the likenesses of real supporters, who have submitted a head and shoulders photo, for a fee. The paper says some of the money would go towards the NHS.
The scheme is set to make its debut in a match in the top German league this afternoon, watched by millions around the world, and thousands of recyclable fans in the stadium.