Internet providers are under pressure to do more to help low-income families afford data packages for their children to take part in remote learning.
It follows a decision to close UK schools to most pupils to enforce new coronavirus lockdowns.
The children's commissioner for England told the BBC that "broadband companies really need to step up".
Labour leader Sir Keir Starmer added he thought the cost of data was "a big problem".
"We're asking people to endure very tough restrictions. And there has to be the other side of that contract," he told BBC Radio 4's Today programme.
"Everybody needs to try and make this work. And that includes the companies that can take away the charging for data. It's a serious situation."
When questioned about the topic at a Downing Street press conference, Prime Minister Boris Johnson said: "We are looking at... the potential costs to parents of online teaching, and we're going to do our best to support them in any way that we can and to work with the internet companies."
There is concern that some disadvantaged pupils are currently dependent on pay-as-you-go or monthly mobile phone subscriptions that only include a small data allowance because their families cannot afford or otherwise obtain a separate fixed broadband connection.
"There are 25 million pay-as-you go customers in the UK, and about seven million of those struggle with the cost of topping up their data," commented Chris Thorpe from the Centre For The Acceleration Of Social Technology charity.
Many schools are using video-chat software including Microsoft Teams, Zoom and Google Meet to live-stream classes, assemblies and other activities, which all benefit from a fast, stable connection and can consume a lot of data.
In addition, other tools including Google Classroom, Tapestry and Class Dojo are used by pupils to submit schoolwork and receive marks and other feedback.
The situation became more pressing after the prime minister announced last night that England's lockdown would mean schools and colleges would remain closed to most pupils until at least the February half-term.
Tech for UK - a coalition of technologists and other concerned business leaders - has suggested one way forward would be for internet providers to "zero rate" edtech apps and websites, so that their data use would be deducted from a mobile subscriber's monthly allowance.
However, it acknowledges the challenge in doing so is to pick which platforms to support without giving some providers an unfair advantage over others.
The Department for Education already runs a scheme for disadvantaged children who do not have access to a home broadband connection to temporarily increase their mobile data allowance.
In some cases, this involves an extra 20 gigabytes a month. In others - such as Three - it provides an "unlimited" data upgrade.
Schools, trusts and local authorities need to request the support on a pupil's behalf.
The networks involved in the initiative include:
- Virgin Mobile
- Tesco Mobile
- Sky Mobile
In cases when this is not available, the government offers 4G wireless routers - which use mobile networks to offer a wi-fi connection - as an alternative.
In addition, Vodafone provided 350,000 "free data" Sim cards to thousands of primary and secondary schools and colleges in November.
"We are actively considering what to do now about this new situation," it said.
O2 pledged in October to donate 10,000 devices and 12 months of free data to "vulnerable individuals".
And Virgin Media noted it had launched a discounted home broadband service for families facing financial difficulties and receiving universal credit.
BT says it has already removed all caps on its home broadband plans to help ensure children can stay connected to their schools.
Anne Longfield, the children's commissioner for England, said she was also concerned about the provision of devices.
"A lot of children still don't have laptops. They're surviving on broken phones," she told the Today programme.
The Department for Education said it had delivered more than 560,000 devices to schools and councils in England between the start of the pandemic and the end of last year.
In addition, it aims to have delivered a further 100,000 laptops and tablets to schools by the end of this week to help get closer to its overall target of one million devices.
However, teaching groups have raised concerns about the rollout.
"We must hear no more of rationing of equipment, as we did late last year," Dr Mary Bousted, joint general secretary of the National Education Union (NEU) told the BBC.
"If the stockpiles exist, as the Department for Education claim they do, then they must be distributed urgently. We have heard too many stories of requests from schools not being met, or not being fully met."
Steven George of head teachers' union, NAHT added that a website used to order laptops had been inaccessible over the Christmas break, so some members had been unable to make requests.
In addition, the Association of School and College Leaders suggested the government had "never really got to grips" with the issue.
"It is certainly sending out lots of laptops for disadvantaged children to schools. But there's clearly still a gap, not just in terms of the number of devices that are required but also in terms of whether families have sufficient connectivity," said general secretary Geoff Barton.
"This has happened because it is a crisis situation, and there hasn't been a great deal of time in which to properly assess the level of need that exists, but it does expose the fact that pre-crisis, there hadn't been a properly joined-up national strategy on digital learning."
Others have noted that the device allocation scheme does not extend to printers - which are needed for worksheets and other materials sent by teachers - putting low-income families at a further disadvantage.