Government scientific advisers have cast doubt on the safety of opening schools up to more pupils in less than a fortnight as the list of councils saying their primaries will not open lengthens.

Last night, epidemiologist Professor John Edmunds was asked what needed to be place before schools could safely be reopened.

“I think the first thing we need to have in place is a well-functioning track and trace system,” the member of Sage (the government’s Scientific Advisory Group for Emergencies) told Sky News.

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“That needs to be embedded, it needs to be clear that’s working well. Without that, I think there is a risk that we would return to a situation where the epidemic might increase.”

His comments echo warnings from local public health officials. The government has admitted that its smartphone tracing app has been delayed and is now not expected to be ready before primary schools are set to open to pupils in three year groups on 1 June.

Pensions secretary Thérèse Coffey said yesterday that the app would be ready in the “coming weeks” and that no condition had been set for it to be established before primary pupils return.

But last night, a senior government scientist seemed to imply that ministers had been advised that they should not set a fixed date for school openings and that a track-and-trace system should be in place first.

Appearing at the daily Downing Street briefing, Professor Dame Angela McLean (pictured), the government’s deputy chief scientific adviser, was asked whether it was too early to conclude that the science says it is safe to return to schools.

She replied: “Scientists have been clear in our advice that changes to lockdown as we modelled them need a highly effective track, trace and isolate system to be in place.

“And we were also very clear that changes to social distancing measures should be based on observed levels of incidence in places that there’s going to be change, not on a fixed date”.

She was then asked whether track and trace would be fully in place by 1 June - when more primary pupils are set to return to school - and whether that would affect her advice to the government.

Professor McLean said that a full update on the expected rollout of track and trace was expected on Thursday.

The scientific doubts cast over the 1 June opening date came as it was reported that the list of local authorities saying that not all their primaries would comply had grown to as many as 18.

As Tes revealed yesterday, they include Birmingham - one of the country’s biggest. Near neighbour Solihull has become the first Conservative-led council to break ranks.

Leader of the council, Ian Courts, said: “The government has the ambition of a 1 June return, but the reality in Solihull is that schools will need to use that first week in June to ensure they are completely ready for more pupils to attend.

“So places may only be available from the week beginning 8 June.”