Andy Burnham would promise to increase taxes on companies that failed to pay their staff a new £11 living wage if he leads Labour into the next general election.

The leadership candidate will set out his plan on Monday at a campaign event in Pudsey, a Yorkshire constituency that Labour failed to win in May, as he begins the final 10 days of campaigning.

Burnham will say that his living wage will be applied to all age groups, adjusted for the loss of tax credits and linked to the cost of housing, food and household items. It would be set at about £11 nationally, and more than £12 in London, and would be a priority for a Labour government led by Burnham in 2020.

He will say that to incentivise the country’s businesses to pay the higher wage he would allow them to sign up to pay lower national insurance contributions. Those that failed to pay it would face penalties and higher contributions in a carrot and stick approach.

Burnham has already pledged to ensure that all workers are eligible for the minimum wage. From 1 October those under 18 must be paid at least £3.87, or less if they are an apprentice. Those 21 and over will receive £6.70 or more.

The shadow health secretary, who is believed to be running second in the contest behind Jeremy Corbyn, will say that the government’s pledge for what it referred to as a national living wage of £9 an hour by 2020 was an attempt to fool voters.

He will say: “Osborne’s so-called national living wage is a complete con. Millions of young people will miss out and be at greater risk of exploitation in the workplace. Because Osborne’s wage only applies to people aged 25 and over, it will create a two-tier workforce.

“It will make it even harder for young people losing their tax credits to get on in life and widen the divide between young and old even further. Osborne needs to think again.”