Robert Jenrick, the housing, communities and local government secretary, has “made it clear” to councils that they must keep parks open during the coronavirus lockdown, although he sidestepped calls to apologise for visiting his Herefordshire home.

Speaking at the daily Downing Street press conference on the coronavirus outbreak, Jenrick said it “cannot be right” that some councils across the country had closed their parks in recent weeks.

He said that, while the virus “does not discriminate”, lockdown measures are much harder for people who do not have gardens or open spaces for children to run around in.

“People need parks. That’s why I have made it clear to councils that all parks must remain open,” he said.

The announcement comes weeks after the health secretary, Matt Hancock, threatened a ban on outdoor exercise on the weekend that Brockwell Park, in south London, was controversially closed in response to a reported influx of sunbathers. Analysis by the Guardian has revealed that park closures would disproportionately effect the most deprived Londoners.

Jenrick also addressed reports of mourners being turned away from funerals, pointing to the case of 13-year-old Ismail Mohamed Abdulwahab, from Brixton, who died after contracting Covid-19.

He said the tragedy was compounded after Ismail’s family could not attend his funeral. “That is not right and it shouldn’t have happened,” he said. “For clarity, funerals can go ahead with close family present.”

The government will publish further guidance on funerals, Jenrick said, adding: “I’m also asking councils to keep open or indeed to reopen cemeteries and graveyards ... for people to make that private visit and seek solace at the grave of someone you’ve loved or to privately lay flowers.

“There have been times in my life when I have needed to do that. These are small steps, but small mercies can make a difference.”

Jenrick defended his decision to visit his parents’ home earlier this month, despite repeatedly urging the public to stay at home to curb the spread of coronavirus.

The Guardian established that the housing secretary visited his parents in Shropshire, 40 miles from his own home by road, who were already being supported with grocery deliveries by their local community.

Jenrick said in the briefing he had delivered medicines to his elderly parents and that it is “entirely within the guidelines” to do so.

He said he “would not want people to feel concerned that they cannot do something like that to help their own elderly relatives or parents who are in need”.

Jenrick was also asked whether he should apologise to the public for seeming to have broken the rules when visiting his Herefordshire home during the lockdown. He says his house in Herefordshire is his main home, despite the fact his children and wife attend school and work in London.

He responded: “I joined my family at our home in Herefordshire as soon as I was able to do so, as soon as we made the decision that it was no longer necessary to work in person in Westminster.

“I’ve been there since I’ve been working from home and returned to Westminster last night to do this press conference because parliament returns next week.”

The briefing came as the number of people to die in UK hospitals rose by 888 to 15,464.