A ban on people in England walking or exercising with anyone from outside their household is under “active consideration” sources have told the Guardian, although the health secretary, Matt Hancock, on Monday evening insisted that he did not want to have to tighten the rules. Discussions have taken place in government about returning to the rules of March 2020, which limited people to one form of outside exercise a day – such as a run, walk, or cycle – either alone or only with people you live with. However Hancock said he hoped that the current rules, which allow people to exercise with one other person, would remain. “We are seeing large groups and that is not acceptable,” he said. “This is one of those rules where if too many people keep breaking it then we are going to have to look at it. But I don’t want to do that because for many people being able to go for a walk with a friend, especially if they live alone, is their only social contact. “It is very important people don’t try to flex the boundaries around it,” he added. “Don’t say you are exercising when you are really socialising. We really don’t want to have to tighten it further.” Suggestions that elite sport could be forced to be paused have been played down, although on Monday, Alison McGovern, Labour’s shadow sports minister, warned it was becoming “increasing difficult” to keep elite sport going. “Sport in this country has taken huge measures to ensure games can go ahead and players and fans are kept safe,” she said. “But it’s clear that with cases rising across the country, this is becoming increasingly difficult. Labour has said all along that the government should follow the science – and we implore the government to follow any advice Sage issue.” The Scottish Football Association became the latest organisation to pause its season – announcing a three-week suspension on Scottish Cup games and for clubs below the Championship. Images such as Crawley players crowding together and singing as they celebrated their FA Cup victory against Leeds have concerned ministers, and the message to elite sport is they should not forget they are in a privileged position compared to the rest of the country. However government sources insisted that, despite rumours on social media, there were no plans to tell elite sport they had to stop. Last week the record number of Covid cases prompted the Premier League to speak to clubs about tightening up their safety protocols around training, travel to and from matches, accommodation and at the games themselves. Representatives from the Premier League, English Football League and National League also met Oliver Dowden – the secretary for culture, media and Sport – last week where they were reminded of the importance of adhering to Covid protocols.