Boris Johnson on Monday promised clarity to teachers, parents and pupils on school reopenings in England as soon as possible, as pressure grew from Conservative backbenchers on the government to outline its plan.

The UK prime minister said schools remained a “priority” but argued that lifting restrictions too quickly while the prevalence of the virus remained high could lead to “another great spread of infection”.

Mr Johnson refused to provide a clear date for school reopenings, adding: “I understand why people want to get a timetable from me today, what I can tell you is we’ll tell you, tell parents, tell teachers as much as we can as soon as we can.”

In recent days, the government has come under growing pressure from some of its own MPs after several reports that students may have to wait until Easter to resume in-person teaching.

The plan was for schools to return after the February half-term holiday when their closure was announced in a last-minute U-turn in early January.

Findings from the Office for National Statistics published on Monday showed that teachers are no more likely to die from coronavirus than the rest of the population.

The ONS said rates of death linked to Covid-19 among those in frontline teaching roles in England and Wales were “not statistically significantly raised” compared with others of the same age and sex. The findings were based on analysis of 7,961 deaths in the working age population registered between March and late December of 2020.

The mortality rate among secondary schoolteachers was higher, but the ONS said that it was not statistically significant from that seen in people of the same age and sex in the wider population, or from the rates seen in other professional occupations.

Teaching unions have argued that staff would be put at risk if schools reopened prematurely, pointing to figures on staff absence due to the virus, which they said suggested a much higher incidence of infection than among the general population.

Paul Whiteman, the general secretary of the National Association of Head Teachers, said the death statistics would do little to reassure teachers. “I don’t think it takes us anywhere fast. If you’re putting a workforce in confined spaces with cohorts of the population that are potentially transmitting it’s about giving the workforce confidence.”

He called on the government to do more to plan the details of a full reopening with headteachers, including considering possibilities like rotas or returning only select year groups.

The pressure over schools from some Tory backbenchers underpin their wider concerns about the impact of the lockdown. Mark Harper, chair of the Covid Recovery Group, told BBC Radio 4’s Today Programme: “All we’re asking for at this point is for the government to set out that sort of plan, based on milestones, based on evidence, so that school leaders, parents, children, have some hope and know what to expect.”

On Monday evening, Steve Baker, deputy chair of the CRG, joined senior backbenchers Graham Brady, Esther McVey, Robert Syms and 13 other Tory MPs, in supporting a parent-led group, UsforThem, which is demanding the immediate full reopening of schools or for ministers to publish evidence to justify their closure.

“The UK’s scientific advisers originally opposed school closures, and as recently as August last year [chief medical officer] Chris Whitty said that it is ‘incredibly clear’ that school closures will damage children’s life chances and that ‘many more are likely to be harmed by not going’ to school ‘even during this pandemic’,” said Jonathan Gullis, a member of the education select committee and former teacher, who also backed the petition.

Gavin Williamson, education secretary, is expected to provide an update to MPs in parliament this week and has promised schools will have two weeks’ notice of any change in policy.