Boris Johnson said people will have to be “realistic” about the impact of the new coronavirus variant, amid calls by a large group of headteachers for GCSE and A-level exams to be scrapped this summer.

It comes amid chaos over plans for reopening schools this month due to the Covid-19 crisis, and concerns about the fairness of any exams which could be held.

Asked whether exams should be cancelled, the Prime Minister told The Andrew Marr Show on BBC One: “We’ve got to be realistic, we’ve got to be realistic about the pace at which this new variant has spread, we’ve got to be realistic about the impact that it’s having on our NHS, and we’ve got to be humble in the face of this virus.”

Most primary schools in England are scheduled to open on Monday, followed by a staggered start for secondary schools a week later, with GCSE and A-level pupils set to return first.

Education Secretary Gavin Williamson insists the summer national exams must still go ahead.

But more than 2,000 headteachers, from the campaign group WorthLess? say pupils, parents and teachers should not be put at risk of contracting Covid for the sake of protecting exam timetables.

The level of online learning children in exam years can get and whether schools are closed for a period of time are among the factors which need to be considered in deciding whether exams should be scrapped for 2021, according to Anne Longfield, the Children’s Commissioner for England.

Headteachers are aware that centre-assessed grades may be an alternative and may want additional safeguards around the robustness of decisions.

Ms Longfield told BBC News Channel that children who have exams this year want “clarity”, adding: “Most children I talk to want exams to continue, but clearly they need to be fair.”

The headteachers from WorthLess? were quoted as saying in The Sunday Times: “Wider public health, pupil and staff safety should be prioritised ahead of examinations.

“Public safety should not be risked or driven by an inflexible pursuit of GCSE and A-levels.”

One of the group’s leaders, Jules White, head of Tanbridge House School in Horsham, West Sussex, said there was “great scepticism that exams can now go ahead fairly”.

Recommending teacher assessments for final grades instead, the group says it would be unfair on pupils in areas hit harder by the pandemic than others to go ahead with exams.

They (teachers) are better than algorithms and they are the only people who can possibly assess the achievement of their students in this extraordinary time

Official data cited by the Times shows 62% of pupils were not in school in Medway, Kent, in the last week of November, because they were either self-isolating or ill. But in Southend-on-Sea, Essex, the figure was only 8%.

Former education secretary Lord Baker said teachers should be allowed to provide a school-leaving assessment grade of pupils’ performances – accounting for factors such as number of days missed – rather than having them sit exams.

“They (teachers) are better than algorithms and they are the only people who can possibly assess the achievement of their students in this extraordinary time,” Lord Baker said.

Matt Hood, principal of the online Oak National Academy, which was commissioned by the Government to produce online lessons for teachers’ use, said about a million children had been forced to use parents’ mobile phones to study as they did not own a phone or laptop.

Some parents, however, could not afford the extra data charges incurred and had to stop their children from studying, again highlighting disparities between pupils across the country.