Boris Johnson has said that “tougher measures” may have to be imposed to tighten social distancing rules because of members of the public “heedlessly” congregating in parks and other open spaces in a way that risks spreading coronavirus.

In his latest daily press conference at 10 Downing Street, the prime minister even suggested that curfews and restrictions on movement – as seen in nations like Italy – could be needed to control the outbreak, which has already claimed 281 lives in the UK.

More draconian measures could come shortly, the prime minister suggested, with No 10 considering the next move “very actively over the next 24 hours”.

Mr Johnson said he wanted people to be able to go to parks, but said it was “absolutely crucial” that they follow public health guidance: “Stay two metres apart. It’s not such a difficult thing. Do it.”

Asked if and when he might consider an Italian-style lockdown, Mr Johnson replied: “You’ve got to impose these interventions in the spread of the epidemic at the moment when they can have the maximum effect.

“After all, when the epidemic is hardly spreading at all, that’s not the moment to impose curfews and prohibitions on movement and so on. You’ve got to wait until alas it’s the right moment to do it, and that’s always been how we’ve been guided.”

His comments came amid widespread complaints that people were continuing to congregate in large numbers in shops, parks and outdoor markets, despite advice that avoiding social contacts is the best way to slow the spread of coronavirus and prevent it overwhelming the NHS.

“I want to thank the vast majority of people who are really behaving incredibly responsibly and following the guidance and the advice on social distancing,” said the prime minister.

“The difficulty of course is that what is happening is that some people are – either through heedlessness or whatever – are not making it easy for us, because they are congregating in a way that is likely to spread the disease.

“We have to think very carefully now about how we take steps to correct that. We will be thinking actively over the next few days.

“The best thing that everybody can do, if you are going outside, observe social distancing. Stay two metres apart. It’s not such a difficult thing. Do it.

“And we say to people: stay at home. That’s the best way to protect the NHS. That’s the best way to save potentially many, many thousands of lives.

“The more we comply now, the faster we will beat it and the faster we will get through it.”

Mr Johnson added: “I want – of course I do – people to be able to go to the parks and open spaces and to enjoy themselves. It’s crucial for health, mental and physical wellbeing.

“But please follow the advice and don’t think that fresh air in itself automatically provides some immunity. You have to stay two metres apart. You have to follow the social distancing advice.

“Even if you think that you are personally invulnerable, there are plenty of people that you can infect and whose lives will then be put at risk .”

It comes as the NHS was due to begin sending letters to 1.5 million of the most vulnerable people to urge them to remain at home for the next 12 weeks.

This group, which includes certain cancer patients, people with severe respiratory illnesses and recipients of organ transplants, will be able to access get vital medicines and food from community hubs if they do not have family and friends living nearby.

Standing alongside the prime minister, the communities secretary Robert Jenrick said that free parcels of groceries would be left on people’s doorsteps, adding: “Nobody needs to worry about getting the food and essential items that they will need.”

He said: “I don’t underestimate what we’re asking of people. It will be tough.

“But if you are one of these people I want to assure these people on behalf of the government that you are not alone.”

On Sunday, NHS England announced that one of the victims was just 18 years old.