Jeremy Corbyn will switch the focus of Labour’s campaign to education on Friday with a speech in Wales, warning that too many schoolchildren are “crammed into classrooms like sardines”.

The Labour leader will visit the Conservative constituency of Cardiff North where he will claim that “seven years of Tory failure and broken promises have left our schools in a terrible state” and that “hundreds of thousands of our children are paying the price”.

He will point out that the Tories have failed to deliver the 2010 manifesto pledge to deliver “small schools with smaller class sizes”.

Corbyn will promise: “Labour will stand up for all children by building a schools system for everyone, keeping class sizes down and making sure schools and teachers have the resources they need to ensure that every child, whatever their background, has access to a world-class education.”

Labour party analysis of Department for Education figures suggests 40,000 primary pupils are being taught in classes of more than 36 pupils and 16,600 are now in class sizes of 40 and above.

Angela Rayner MP, the shadow education secretary, said: “This situation is becoming unsustainable; too many children are being taught in classes which are simply too big.

“The system for school place planning is broken. The Tories need to let go of their unjustified fixation with free schools, but instead they have relaxed the rules so even more can be built in areas where there is no demand for places. Free schools are clearly not addressing the growing pressures on schools.”

Labour believes that pushing the class size issue, together with its recent free school meals pledge and its opposition to the creation of new grammar schools, means that ut has a strong story to tell about education. However, it will not be clear until its manifesto is published how increased spending on schools will be funded.

The Conservatives responded to Corbyn’s plan to go on the offensive over education by drawing attention to Labour’s record in Wales, where it oversees education as part of a coalition with the one Liberal Democrat assembly member.

“This is a massive own goal from Labour. In Wales, where they administer schools with the Lib Dems, the numbers of infants in large classes has risen by 18% in just three years,” a Conservative spokesperson said.

Corbyn’s visit to Cardiff North, a seat held by Conservative MP Craig Williams with a majority of 2,137, reflects Labour’s determination to show that it is optimistic about gaining seats, despite trailing Theresa May’s party by more than 20% in some polls.

Labour is keen to shift the debate in the election campaign away from the issue of Brexit, which divides its voters, and focus instead on the government’s record on public services and living standards.

Funding cuts for schools have caused disquiet among parents in many areas, with Conservative backbenchers among those expressing concerns.

Corbyn launched Labour’s campaign with a bullish speech on Thursday, characterising the 8 June election as a straight choice between the Conservatives as “the party of privilege and the richest” and a Labour party fighting for everyone. “It’s the establishment versus the people, and it’s our historic duty to make sure the people prevail,” he said.