Sadiq Khan is to make a campaign for wide-ranging rent control the key plank of his 2020 re-election bid, asking the government to give the London mayoralty the power to combat soaring rents in the capital.

The mayor of London is to work out a blueprint for an overhaul of the laws for private renters to allow new restrictions on rent to be imposed – a change he could not make without legislation by central government.

Khan told the Guardian the arguments for rent control were “overwhelming and Londoners overwhelmingly want it to happen”, but said he could not make the change within his current remit.

“London is in the middle of a desperate housing crisis that has been generations in the making,” Khan said.

“I am doing everything in my power to tackle it – including building record numbers of new social homes – but I have long been frustrated by my lack of powers to help private renters.”

Recent YouGov research by City Hall, released to the Guardian, suggests that two-thirds of the 2.4 million renters in London, more than a quarter of the city, are strongly in favour of pricing controls.

Average private rents in London rose by 38% between 2005 and 2016, with prices for an average one-bedroom rented home in London higher on average than for a three-bedroom home in every other English region.

However, it is a plan not likely to find favour with the Conservative government. The housing secretary, James Brokenshire, has argued that the controls would lead to poorer housing standards, with landlords unable to afford to maintain properties, and could also have a dramatic effect on housing supply, with landlords choosing to sell up rather than have their rental income reduced.

The blueprint for rent stabilisation and control laws will be devised by Khan’s deputy mayor for housing, James Murray, and the Westminster North MP, Karen Buck, who last year won government support for her private member’s bill to put legally binding standards on rented homes.

“London’s private renters are among the worst affected by the housing crisis in the capital, and the laws to protect them are woefully out of date,” Buck said.

“We need an approach to rent stabilisation and control that works in London. Once we have set out these proposals, we will argue the case that ministers must support London’s private renters by putting our plans into action.”

Most major cities in Europe and North America have some limits on rents in the private sector. In Berlin, rents are controlled both within and between tenancies and New York has some apartments capped by the NYC Rent Guidelines Board, while others have their rent “stabilised” or reset between tenancies.

In Scotland, new laws have recently been introduced to allow councils to apply to implement “rent pressure zones”, where rent increases are capped at no higher than inflation.

Hannah Slater, policy manager at the campaign group Generation Rent, said Londoners would welcome any possible changes.

“Londoners are paying some of the highest rents in the world and many are struggling to keep a roof over their head in the area they grew up in or close enough to where they work,” she said.

“Unaffordable rent increases force people into stressful moves away from neighbourhoods where they have roots, thereby eroding London’s communities. Renters need stability in our homes that can only come from certainty over what rent we pay – but we need to [be able to] afford a home in the first place.”

Khan will face a Conservative challenge from Shaun Bailey, who has been a critic of Khan’s housebuilding record because of numerous delayed housing schemes in the capital, though Labour has blamed Brexit for the construction slowdown and argued the mayor has overseen the building of more new homes in one year than any of his predecessors.

Brokenshire’s spokesman said Khan was not using his existing powers to build more houses.

“The mayor came into office saying he’d sort out London’s housing market; instead what he’s overseen is an eye-watering drop of 20% in new-build starts,” the spokesman said. “If he can’t use the powers he does have effectively, why on earth would Londoners trust him with more?

“People who want a more affordable and secure private rental market thankfully don’t need the mayor’s help because they can trust the Conservatives in government to watch their backs.”

Labour’s 2017 manifesto included a pledge to “introduce controls on rent rises” and to consider giving the mayor of London additional powers, given the particular pressures in the capital.

Previously the party had promised legislation decreeing that landlords would only be able to raise rents for tenants by less than inflation for the duration of a contract.