Boris Johnson is facing pressure to make a speedy return to work, as fresh data suggests the onset of lockdown fatigue, and as senior police officers argue over rules on movement.

Warnings for the public to continue respecting lockdown rules were sounded at Friday’s Downing Street briefing, where data showed that there had been an increase of between 2% and 3% in transport use over the past week.

While driving and journeys on public transport have remained consistently low, data from Apple reflecting requests for directions also suggested that there had been an uptick over the past week in terms of people venturing out on foot in London.

On Wednesday, the government’s own figures had shown that the UK’s vehicle traffic levels this week were at their highest since the country’s lockdown began.

The transport secretary, Grant Shapps, added that the country had “done incredibly well” but warned: “There is a danger as we go into another warm sunny weekend that people think that the peak is over – but it is not over. We are riding perhaps, we hope, a downward trend but it is by no means established yet.”

The deputy chief medical officer for England, Jenny Harries, said: “On the whole, as we have just seen, most of the public are really complying and really do support [social distancing]. That becomes increasingly difficult as we go through.”

The data on transport use came as a senior police chief criticised national police guidance on exercise rules as hundreds of people in south-west England flouted lockdown restrictions to enjoy 20C sunshine.

While updated guidance from the National Police Chiefs’ Council stated that driving to the countryside and walking was considered a “reasonable excuse” for people to leave their homes in England, it was criticised by the Chief Constable of Devon and Cornwall police, Shaun Sawyer, who said people should not drive to go exercising, dog walking or surfing.

“The National Police Chiefs’ guidance, which I think is some of the poorest guidance I have seen for a long time sadly, would allow people from outside the force [region] access to come in, the very thing that our communities don’t want,” he added.

His comments came as calls for the prime minister to return to the helm of government grew louder on Conservative backbenches.

Andrew Bridgen, the MP for North West Leicestershire, said: “There are huge decisions that are going to have to be made in the near future and that can only be done by the prime minister. Boris can carry the public with him, he is the leader of the party with a huge election victory.”

Bridgen said detail on easing lockdown restrictions for businesses and more information on when schools might go back would be top of Johnson’s in-tray.

Facebook Twitter Pinterest Grant Shapps, the transport secretary, urged people to abide by lockdown restrictions during his press conference at Downing Street. Photograph: Pippa Fowles/10 Downing Street/Crown Copyright/PA

Another Tory backbencher said Johnson’s absence had put significant strain on the government and lead to people taking the daily press conferences who did not have his skills.

“There is a sense that people do want him back mainly because the people who have stepped in have maybe not performed as well as he could have done,” they said.

“I’m thinking of the press conference [of the business secretary] Alok Sharma took, and Priti Patel’s [home secretary]. There is a sense it’s much better to have one person that everybody knows as the focal point and that the people brought in on a daily basis have not been as good.

“What this has revealed is that the bench has not stepped up.”

Ministers had been discussing a sector-by-sector approach to lifting the lockdown in recent weeks. However, Whitehall sources say the expectation is now that the focus will be on the nature of the work being carried out: can it be done while maintaining physical distance, and how essential is it to the economy?

The “quad” of senior ministers – Matt Hancock, Dominic Raab, Michael Gove and Rishi Sunak – has also begun work on the preconditions that would have to be in place before workplaces could reopen, including increasing the frequency of transport services, and reopening schools.

Government sources sought to play down divisions over what happens next. “Most of the cabinet are in a pretty similar place: everybody wants the lockdown to end as soon as possible, but we have to do it at the right time,” said one adviser.

Greater Manchester police thanked the public following what the force said had been a significant reduction in calls to house parties. Officers were called to 432 reports of house parties last weekend, a 52% reduction on previous reports.

Facebook Twitter Pinterest Conservative backbenchers have been calling on Boris Johnson to return to Downing Street. Photograph: Pippa Fowles/10 Downing Street/AFP via Getty Images

But there were hints of a potential unravelling of the lockdown in London, as the city headed into a warm weekend. On social media, Londoners reported seeing more traffic on the roads and more people using parks for more than just brief exercise.

The latest “Covid‑19 mobility trends” data from Apple, which reflect daily requests for directions in Apple Maps, suggested that walking by Londoners was starting to tick up for the last three weekends compared with the first day of the lockdown.

Weekdays in the last two weeks had also seen slightly more movement. Driving and public transport usage was consistently lower.

More reassuringly, recent data from Transport for London showed levels of movement on public transport in the capital this week were broadly as they were last week.

On the underground and buses, ridership was still down 95% and 85% respectively compared to the same time last year. A spokesperson for London’s mayor, Sadiq Khan, said: “Sadiq has been absolutely clear that unless Londoners are making an essential journey, they should stay at home to save lives. The vast majority of Londoners have followed this advice.”

Speculation over Johnson’s imminent return to work grew after Donald Trump said he had sounded “incredible” and “ready to go” in a phone call with him following his discharge from hospital.

A report in the Daily Telegraph suggested Johnson, who has been recuperating at Chequers, could return to work on Monday. While Downing Street said the PM was yet to work on his “red box” of official papers as usual, his official spokesman said he was regularly receiving updates on the coronavirus response and had had calls with Raab, the foreign secretary, and Hancock, the health secretary.

However another Tory told the Guardian the prime minister should not rush back to work as other ministers were coping.

They said: “For Boris there’s no rush and the priority is that he has got to be fully ready. Matt Hancock has been a hero throughout this and worked tirelessly.”

Additional reporting by Alex Hern and Caelainn Barr