John McDonnell has committed a Labour government to raising the living wage to at least £10 by 2020 as part of plans to tackle the “scourge” of low pay.

He told conference that the next administration would set up a special body to deliver a “real living wage”, based on the cost of living, following George Osborne’s previous attempt to claim he was raising the measure, which derided because it merely adjusted the minimum wage.

McDonnell, who is Jeremy Corbyn’s closest political ally, made the pledge as part of a policy-heavy speech in which he pledged to borrow money for a national investment bank, campaign for a fair Brexit and preside over an “entrepreneurial state” to deliver more widespread prosperity.

The shadow Chancellor put the surprise announcement at the centre of his keynote speech at Labour conference.

The national living wage of £7.20 for people aged 25 and over, set out in Osborne’s summer 2015 Budget, came into force earlier this year and prompted a flurry of arm-waving from Iain Duncan Smith, when both men were still in the Cabinet.

Today McDonnell made a wide-ranging address in which he attacked the Tories over the failure on deficit reduction, re-iterated his commitment to bring back sectoral collective bargaining and said Labour would establish a Living Wage Review Body.

“Under the next Labour government, everyone will earn enough to live on. When we win the next election we will write a real Living Wage into law…

“Independent forecasts suggest that this will be over £10 per hour. This will be a fundamental part of our new bargain in the workplace.

“But we know that small businesses need to be a part of the bargain. That’s why we will also be publishing proposals to help businesses implement the Living Wage, particularly small and medium-sized companies.

“We will be examining a number of ideas – including the expansion and reform of Employment Allowance – to make sure that this historic step forward in improving the living standards of the poorest paid does not impact on hours or employment. Backed up by our commitment to investment, we will end the scourge of poverty pay.

“Decent pay is not just fundamentally right, it’s good for business, it’s good for employees, and it’s good for Britain.”

McDonnell criticised the Tories for having “no plan whatsoever” for Brexit and vowed to tackle public concern over EU migration, which played a major part in the EU referendum campaign, and is tied to access to the single market.

A host of Labour figures, including Chuka Umunna, have questioned whether Britain would remain in the single market if it means the perpetuation of free movement of labour and today McDonnell said he would listen to voter scepticism.

“Let’s get it straight, we have to protect jobs here. So we will seek to preserve access to the Single Market for goods and services. Today, access to the Single Market requires freedom of movement of labour. But we will address the concerns that people have raised in the undercutting of wages and conditions, and the pressure on local public services.”