There are concerns some schools in lockdown could be inundated with pupils without laptops after a change to the vulnerable pupil list.
Pupils are learning remotely in England after schools were closed on Tuesday to all but children of key workers and those deemed vulnerable.
But those without laptops or space to study are now eligible to attend school, under government guidance.
Heads' union, NAHT, said the move could reduce the effect of the shutdown.
Schools were ordered to close to most pupils as a way of limiting the spread of the virus.
National Association of Head Teachers general secretary Paul Whiteman said demand for key worker and vulnerable places in schools had risen substantially since the last school shutdown.
Nearly a third of the 2,000 head teachers who joined an online union meeting on Wednesday afternoon reported having between 20 and 30% of pupils in school, the NAHT said.
Mr Whiteman said: "It is critical that key worker child school places are only used when absolutely necessary to truly reduce numbers and spread of the virus.
"We have concern that the government has not supplied enough laptops for all the children without them and so has made lack of internet access a vulnerable criteria - only adding to numbers still in school.
"It is important that all vulnerable pupils have access to a school place, but the government must provide laptops and internet access for every pupil that needs one, so that they can access home learning to take some of the strain off the demand for school places.
"Nearly half of head teachers who we polled during a webcast on Wednesday evening said that had received fewer than 10% of the laptops they'd requested.
"It is essential that this is rectified immediately, so that we can keep school attendance figures at a level which will have the desired impact on getting transmission rates under control."
'Fully open schools'
Jane Girt, head teacher of Carlton Bolling College in Bradford, said the rule change could leave her having to accommodate an extra 200 pupils on top of those already on the key worker and vulnerable children list.
She told BBC News that having so many pupils in school would "defeat the object" of closing amid the England-wide lockdown.
Mrs Girt said her secondary, which has more than 1,500 students, had received 261 laptops from the government since March but about 50% of pupils were sharing a device with another family member.
The prime minister told MPs on Wednesday that 560,000 devices had been given out to schools in 2020 and a further 50,000 so far this week.
And Gavin Williamson reiterated that those without access to remote learning via digital devices could attend school.
He said: "Schools are much better prepared to deliver online learning, with the delivery of hundreds of thousands of devices at breakneck speed, data support and high quality video lessons."
But Ofcom estimates there are up to 1.5m pupils without digital devices in their homes, on which they can learn.
Amanda Bailey, director of the child poverty commission in north-east England, said pupils without internet access tended to be concentrated in disadvantaged areas and this meant some schools would be "largely fully open", she said.
"And we know that the most deprived communities are the ones most vulnerable to the health impact of the pandemic," she added.
"Our main concerns are that we're now nine months into this situation and we're still talking about families not having sufficient access to digital devices or data or the internet."
'National plan needed'
Labour Councillor Beverley Momenabadi, Wolverhampton's champion for digital innovation, said the guidance massively expands the number of children who are entitled to go into school.
She said although plans to support those needing access while self-isolating in her city are at an advanced stage, with rental schemes being accessed and donations sought, the new lockdown changes the game completely.
She called for a national plan for the transition to remote learning.
Councillor Momenabadi said: "Even after Gavin Williamson's statement in the Commons, children across the country are still waiting for that national plan.
"And even on the devices they've said will arrive; how will these be distributed, when will they arrive, will they arrive in time to ensure that no child misses out on their education?"
Will you have to send your child back to school because you are unable to supervise home learning? Or are you a teacher concerned about lack of equipment? Email firstname.lastname@example.org.
Please include a contact number if you are willing to speak to a BBC journalist. You can also get in touch in the following ways: