In an open letter to Gavin Williamson, more than 50 MPs and peers have said urgent action is needed to prevent the poorest pupils falling behind long-term.
Two thirds of secondary schools teaching the most disadvantaged communities are in the north of England, new figures show.
The parliamentarians, including Tories in northern constituencies, are demanding that funding for one-on-one tuition be provided to these pupils when they return to school.
They say in the letter: “The most disadvantaged children fall behind their peers over a long summer holiday, and the shutdown will widen the north’s disadvantage gap and with it the north-south education divide.
“We need to deal with the consequences of this crisis for the most vulnerable in our society, and that must include children from low-income households.”
They say a “catch-up premium” of at least £300m – equating to £700 for every pupil on free school meals – would fund 30 minutes of tuition three times a week for 12 weeks.
The government has refused to say when schools may start to re-open, but sources say the earliest date being discussed is the beginning of June.
Mr Williamson has said there are no current plans for schools to stay open during the summer holidays to help pupils catch up on the lesson time they have missed, and suggested that enforcing social distancing in schools would be challenging.
While some schools have remained open to teach the children of key workers and those who are most vulnerable, officials figures show turnout last week was below 2% of all pupils.
Sky News has highlighted the difficulties for large numbers of families in accessing online lessons since schools closed a month ago.
In some schools, headteachers say up to 40% of their pupils live in a home with no computer, while many more children have to share one device with parents and siblings.
Mr Williamson announced a week ago that the government would provide laptops and internet access to some children – those identified by their school as having a social worker, or disadvantaged pupils taking their GCSEs next year – but there is no timescale for the scheme.
Signatories to today’s open letter include Lord Jim O’Neill, who served as a Treasury minister under David Cameron, and some newly elected Tories in former Labour seats.
They cite research from the Northern Powerhouse Partnership showing pupils in the north are most likely to be from the economic and ethnic groups who make the slowest progress at secondary school including white working class boys and girls.