Labour would create a new department to tackle the housing crisis, Jeremy Corbyn will pledge at the latest rally on his tour of marginal seats.

The Labour leader is touring the home counties on Monday, visiting Reading and addressing a crowd in Milton Keynes, where Labour came within 1,915 votes of ousting the Conservative MP Mark Lancaster.

Corbyn will set out plans to tackle issues affecting commuters, including soaring house prices and the cost of rail travel. Milton Keynes tops the list of towns with the highest price growth over the past 30 years, according to Halifax.

Corbyn will say house prices in the town have risen by 50% in the last five years. “The Conservative government has spent seven years giving tax breaks to the wealthy, who don’t need them, while making it harder for most people in our country to make ends meet,” he will say.

He will reiterate his party’s manifesto pledge to create a department for housing to ensure 100,000 new homes are being built each year by the end of the parliament, should Labour win the next election. “Housing should be about homes for the many, not investment opportunities for the few,” he will say.

Commuter season tickets will also come under fire in Corbyn’s speech. A typical 12-month season ticket fare for a Milton Keynes’ commuter working in London currently costs £5,028.

“Commuters from Milton Keynes to London have seen rail fares increasing

faster than their wages year in, year out,” Corbyn will say. “Labour will bring down

fares by returning our rail system to public ownership, putting more money in people’s pockets and making sure our railways are run in the interests of people, not profit.”

Corbyn’s summer tour of marginal seats has been attracting hundreds of supporters for rallies, despite them often being held on working days.

Similar incursions into Tory marginals are planned for the rest of the week to the north-west of England, including Copeland, which was snatched from Labour by the Conservatives in a byelection this year.

Corbyn will spend the following week in Scotland, holding rallies in SNP-held seats.

He told the Guardian last week in Bristol that he hoped the tour would help the party build a more detailed manifesto for the next election campaign. “Our next election manifesto will be more detailed because we’ll have more time to prepare it, but it will be a reflection of the wishes and aspirations of a lot of people who you’ve never heard of, all around the country,” he said.

“Yes, I’m spending the summer campaigning around the country, but everywhere I go I make sure I have time to meet and listen to different people and different groups, and I learn a lot by that. It does mean that when we’re writing policy documents you think, hang on, this isn’t practical, it wouldn’t work. Let’s do something else.”