The government has been urged to consider making it compulsory for vulnerable children to go to school during the Covid-19 lockdown, as it emerged that teachers were making hundreds of phone calls a week to keep track of at-risk pupils.

The children’s minister, Vicky Ford, faced a barrage of questions from MPs on the education select committee on Wednesday after official government statistics revealed that just 5% of vulnerable children who were entitled to a place in the emergency schools still open during the coronavirus crisis were turning up.

Tom Hunt, Conservative MP for Ipswich, questioned whether it should be left to parents to decide whether or not their children attend school. “It could be the case that sometimes these parents are part of the reason why the child is vulnerable,” he said.

“It does seem as though the government needs to take stock of this and potentially consider making it a requirement that all vulnerable children should be at school.”

While many teachers are worried about low attendance, others say the word vulnerable covers a wide range of circumstances. According to the government definition, it includes children with a social worker or an educational, health and care plan for those with special educational needs.

“I am frustrated with this notion of the headlines that suggest that they must all be in school,” said Caroline Barlow, head of Heathfield community college in East Sussex. “Not all vulnerable students are vulnerable because of their immediate family and many are better at home right now.”

Other school leaders said attendance may be low because the message to vulnerable families is confused – on the one hand they are urged to stay at home in order to be safe, while on the other they are being encouraged to send their children to school.

“It’s a concern that there are low numbers,” said Rachael Warwick, executive headteacher of the Ridgeway education trust in south Oxfordshire where just a handful of vulnerable pupils have been attending school. “But the public health message has been so strong.”

Alison Finley, safeguarding lead and assistant principal at Crawshaw academy, a secondary school with 1,000 pupils in Pudsey, West Yorkshire, bought 20 cheap mobile phones for her team just before lockdown. Since then she and colleagues have made 1,500 phone calls to vulnerable families and 58 home visits.

“The majority said they did not want to come in to school. Some of them said they felt they could look after [their children] better at home. They said it was too dangerous for them to come in to school and their children were too worried.”

With 10 or fewer vulnerable pupils in school, staff are making regular phone calls home. The highest-risk families are called daily, those that are of concern but are lower risk are called three times a week, while others are contacted once a week.

Where concerns are raised, staff pay a home visit. “Ultimately you have to go out and find them. So far we’ve made contact with every single student,” said Finley, who said there had been an increase in domestic violence and mental health problems in families.

Stuart Lock, the head of Advantage Schools trust in Bedford, which runs a primary and secondary school, said the key issue was the safety of pupils, whether they were staying at home or coming to school.

“We know for a small minority of pupils, they find their home circumstances difficult. When we set work online, we get pupils to check in with an online form every day by 9.30am. This invites them to tell us whether they and everyone in their family are safe and well and we can chase up if they say they are not.

“We also have a very small number of pupils who we have in school because it supports their families and they are particularly struggling – but this doesn’t apply to the majority of pupils who we might consider vulnerable. Our pastoral staff in each school also make telephone contact with pupils and families where we know we have had concerns in the past.”

Ed Vainker, executive principal of the Reach Academy Feltham, an all-through school in Hounslow, said: “We have gone from 5% of looked-after children and those involved in social care in school before Easter, to 35% this week. We wanted to get those pupils into school once things settled and we had a strong steer from the local authority to get them back in.

“I do think the numbers in school are only one piece of the puzzle - we are speaking to our vulnerable pupils and their families daily. We are also distributing 2,000 meals weekly, and we are checking in with those families and others very regularly.”

Addressing MPs’ concerns, Ford said: “People are very concerned that they don’t want to get coronavirus and I can absolutely understand that.

“We make it very clear that children who have a social worker are expected to attend school. And if they are not, their schools are working with their social workers to make sure we have eyes on them, that they get visits – whether or not that’s a physical visit, a doorstep visit, a house visit, or a digital visit – depending on the risk to that child.

“Just because the attendance at school may be low that doesn’t mean that those children are not being safeguarded in other ways.”