The Good Law Project is to take legal action against councils over access to education by children from low income families during the lockdown.
It is expected to first take a test case against the London Borough of Southwark and if successful plans a ‘second wave’ of actions against other councils.
The action concerns whether children have access to the tablets or computers needed to keep up with their education.
Think tank the Institute for Public Policy Research has estimated that one million children from lower income households do not have adequate access to a device or connectivity at home.
The Good Law Project - which undertakes pro bono work - said section 19 of the Education Act 1996 placed an obligation on local authorities to provide a suitable education for children, whether inside or outside school.
With classroom teaching replaced by online methods this meant that all children must be provided have access to computers and the internet.
It said the case will be made on the basis of the Education Act 1996, supported by the Human Rights Act, the Equality Act and the UN Convention on the Rights of the Child.
If the action succeeds, the project said the Government should help local authorities to meet the costs as they were operating without clear guidance on access to online resources for the most disadvantaged children.
Good Law Project director Jo Maugham QC said: “The best available estimates are that around a million children in England alone will be unable to access the teaching Government intends should be provided online.
“That's why Good Law Project is crowdfunding the costs of legal action to ensure kids in the poorest families aren't left behind.
“Parliament has decided legal responsibility falls on local authorities but we have also written a pre-action letter to the secretary of state for education asking him to set out his plans, including funding plans.”
Mr Maugham said he hoped the case would be taken forward urgently, and determined in time for the start of the summer term on 20 April.
A crowd funding page in support of the action has so far raised £2,295 towards a target of £25,000.
Cllr Peter John, Leader of Southwark Council, said: “Local government relies on central Government funding, and the taxpayer, for its resources.... It would be more effective for people who can afford to, to back schools and authorities directly, or to ask the Government for more money for resources.
“Aside from this, our schools are making an excellent effort to support children from all backgrounds during this crisis, we will continue to work with them to support adequate digital provision for poorer students, and I agree that access to technology is a huge issue for our children, and something we would welcome further resources from the Government for in the future.”