Customers using BT Mobile, EE, and Plusnet Mobile can use BBC Bitesize content from the end of January without eating into their data allowance.
Bitesize provides structured lessons in maths and English for all year groups, as well as offering other curriculum material.
Content from other providers is likely to be made free in the coming days.
More mobile companies are expected to follow suit in making such content free to use.
The current UK lockdowns mean most children are now learning from home.
- In England, primary and secondary schools have moved to remote learning for most pupils
- In Scotland, schools will remain closed to the majority of pupils until at least 1 February
- In Wales, all schools and colleges will move to online learning until at least the end of January
- In Northern Ireland, many pupils will not return to school until after the half-term break in mid-February
Education Secretary Gavin Williamson has mandated that schools must provide between three and five hours of online content per day.
This has led to concerns that children in families without access to broadband could fall behind.
Schools remain open for children classed as vulnerable and those whose parents are key workers.
All contract and pay-as-you-go customers of BT Mobile, EE and Plusnet Mobile will be eligible and the free package will continue while schools remain closed. No registration is required - the free access will happen automatically.
BT has also asked the Scottish, Welsh and Northern Irish administrations to each suggest one online resource for schoolchildren in its regions, which it will also zero-rate, as the curriculums differ from English schools.
According to UK media watchdog Ofcom, some 880,000 families are reliant solely on mobile connections, and many of those will have data limitations.
BBC director general Tim Davie said: "With the pandemic forcing schools to close again, we should not allow a lack of digital access to further impact children's education.
"The BBC will continue to do all we can to ensure every child, whatever their circumstances, can continue to access vital educational materials during this time."
The corporation is also running three hours of curriculum-based TV programmes alongside the BBC Bitesize collection of educational resources. Primary school programming will be on CBBC, with two hours for secondary pupils on BBC Two.
During the first lockdown, content was available on iPlayer, Red Button services and online, but not on regular TV channels, although viewers in Scotland did have some programming.
BT said the move was part of its wider Lockdown Learning programme.
Other aspects of BT's scheme include:
- unlimited data for some families who can access the scheme via their children's schools
- free wi-fi vouchers, which have been available for customers since June
- a £10-a-month fixed broadband tariff for low-income families
BT consumer brands chief executive Marc Allera said: "We want to ensure that no child is left behind in their education as a result of this pandemic and recognise that we all have a role we can play to help families and carers continue their children's education while schools are closed."