As part of plans to boost skills, the party also said it will restore education maintenance allowance for college students and restore student grants for university students.
Labour said the plans will be funded with £19.4bn that will be raised by reversing the Conservative Party's cuts to corporation tax. Labour has previously said that extending free school meals to all primary age children will be funded by levying VAT on private school fees.
Angela Rayner, Labour's shadow education secretary, said: "Our plans for a new national education service show there is a clear choice at this election.
"Between the Tories who have broken their promises to parents and children, or a Labour party with a real plan for education for the many not the few.
"We will invest in schools and in our young people, ensuring no primary pupils go hungry during the day, reducing class sizes so children can learn and teachers can teach, and restoring the maintenance allowance and grants for students in both further and higher education."
Meanwhile, the Liberal Democrats have said they would invest nearly £7bn more in schools and colleges over the next parliament in order to reverse cuts to frontline school and college budgets, protect per pupil funding in real terms and ensure no school loses out from the national funding formula.
Liberal Democrat shadow education secretary Sarah Olney said: "Children are being taught in overcrowded classes by overworked teachers - but Theresa May doesn't care.
"While funding per pupil is set to see the biggest cuts in a generation, billions of pounds are being spent on divisive plans to expand grammars and free schools.
"This extra £7bn of funding would ensure no school and no child loses out."
Conservative Treasury minister David Gauke described Labour's plans as "yet more chaos" from Jeremy Corbyn.
"Last month he promised them he wouldn't put up corporation tax, now he's hitting them with huge bills," Gauke said.
"While Theresa May and her Conservative team have simplified and cut taxes for small firms, Jeremy Corbyn would drop a tax bombshell on every small business and working family in Britain to pay for his nonsensical policies."