The minimum wage will rise to £10 an hour within months if Labour wins the next general election, Jeremy Corbyn will say on Monday. In a bid to win over voters ahead of local polls in May, the Labour leader is setting out the details of the party’s longer-terms plans for a a higher minimum wage, which will benefit nearly 6 million workers.

Employees on basic earnings would be better off by thousands in 2020 compared with the current expected rate under the government’s “national living wage”.

Corbyn, on a visit to Luton, will say that low pay blights the lives of large and growing numbers in the UK and fuels widening inequality. “The government’s rebranding of the minimum wage to the national living wage hasn’t dealt with the real problems of low pay and rising cost of living,” he will say. “That’s why Labour will raise the legal minimum wage for all to at least £10 an hour by 2020, giving more than five and a half million people a pay rise in the process.

“Labour’s real living wage will immediately boost the incomes and opportunities of more than 20% of the workforce, especially in sectors such as retail, care and hospitality. We know that where work pays, living standards rise and reliance on benefits falls. This is the right thing to do, and a Labour government will be committed to rebalancing our economy so that no one and no community is left behind.”

The Labour policy, first announced last year, would leave full-time employees on basic earnings better off by more than £2,500, while 21- to 24-year-olds on lower wages would be in line for a £4,500 hike. Around 5.6 million workers would see their pay go up. Northern Ireland, the east Midlands and Yorkshire would be among the areas to benefit most, with one in four residents affected, according to the party.

Shadow chancellor John McDonnell said: “Theresa May promised to be a champion of working people; she has failed. The Tories are taking the country backwards; Labour will stand up for working families, making them £2,500 a year better off in 2020.

“Only Labour will take the action needed to end the Tories’ economic failure and introduce a real living wage of £10 an hour by 2020.”

The government has begun to phase in its national living wage, with the aim of reaching 60% of median UK earnings by 2020. For employees aged over 25, the wage will begin at £7.20 an hour in April 2016, and is projected to rise to at least £9 an hour by April 2020.