UK schools are now closed to most pupils as part of the latest lockdown, and the children's commissioner for England has called on companies to "step up" with lots of children needing access to remote learning.
And speaking to BBC Radio 4's Today programme, Labour leader Sir Keir Starmer added: "We're asking people to endure very tough restrictions. And there has to be the other side of that contract.
"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."
Asked about the issue this week during a Downing Street press conference, Prime Minister Boris Johnson commented: "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."
Some disadvantaged pupils are dependent on pay-as-you-go or monthly phone subscriptions - which only come with a small data allowance - because their families are unable to afford or obtain a separate broadband connection.
However, many schools across the country are now using video-chat software - such as Zoom, Google Meet and Microsoft Teams - to stream classes and other activities.
These programmes can use a lot of data and work best with a fast and stable internet connection.
Meanwhile, other tools - including Class Dojo, Tapestry and Google Classroom - are also being used online to let students submit work and receive marks and feedback.
Now, Tech for UK - a coalition including the likes of EE, Three, Virgin Mobile, Tesco Mobile, Smarty and Sky Mobile - has suggested providers could "zero rate" edtech sites and apps, which means their data use would be deducted from a subscriber's monthly allowance.
An alternative has seen the government offer 4G wireless routers, while in November Vodafone provided 350,000 "free data" Sim cards to thousands of schools and colleges.
In October, O2 pledged to donate 10,000 devices and 12 months of free data to "vulnerable individuals", and BT has already removed all caps on home broadband plans.