Jeremy Corbyn has accused the government of being “in the pockets of rogue landlords” and unable to fix what he called a “crisis level” of squalor at the bottom of the rented housing market.

More than half a million people aged under 35 are estimated to be living in rented properties so hazardous they are likely to lead to residents needing medical attention, the Guardian reported on Sunday.

Responding to the story, the Labour leader said: “The squalid and unsafe conditions that hundreds of thousands of people face are at crisis level. The broken housing market is in urgent need of a complete overhaul. The Conservatives can’t fix the housing crisis because they’re in the pockets of property speculators and rogue landlords, not on the side of tenants.”

But the housing secretary, Sajid Javid, has insisted the government is backing greater rights for tenants to take on rogue landlords, amid growing concern at the exploitation of tenants in all parts of the private rented sector but particularly in urban areas with severe shortages of rented homes.

In September he said he would consult the judiciary about the prospect of a new housing court to deliver “faster, more effective, justice” and reassure tenants there was somewhere with the “power to put it right”.

Currently, wronged tenants must rely on councils to take action against bad landlords, but many do not do so. However, even when landlords are successfully prosecuted, some consider fines “part of the business model”, Sir Robin Wales, the leader of the London Borough of Newham, told the Commons communities and local government committee on Monday.

“The problem is quite simply shocking,” Wales told the MPs. “Twenty-five people living in a three-bedroom house is not unusual. There was a guy on a raid I went on sleeping under the stairs. Harry Potter had more room [at the Dursleys’ house]. This is what our country is like in London and in other cities in the country.”

Inside a rented house in Newham that was found to have category 1 hazards. Photograph: Andrew Baker/London Borough of Newham

He is calling for councils to be given powers to confiscate property from rogue landlords. On Monday the Guardian reports on landlords who have been fined over £30,000 by a magistrates court for multiple breaches of regulations, but are continuing to operate an unlicensed house of multiple occupation in Canning Town, east London.

A spokesman for the Ministry of Housing said: “Everyone deserves a safe and decent home and we have given councils strong powers to crackdown on bad landlords and we expect them to use them. We have brought in £30,000 fines, are introducing a database of bad landlords and given councils £12m to enforce the law in hotspot areas. We are also supporting Karen Buck’s private member’s bill which will require all landlords ensure their properties are safe and give tenants the right to take legal action.”

Buck is a Labour backbencher whose housing fitness bill has become the focus of cross-party policy attempts to tackle the squalor problem. The bill would give tenants the power to take landlords directly to court if they were renting homes in disrepair.

Although the government said it would back the bill, in 2016 Javid and the current housing minister, Dominic Raab, were among 309 Conservative MPs who voted against an amendment to the housing and planning bill to “require that residential rented accommodation is provided and maintained in a state of fitness for human habitation”.

The government said it would result in unnecessary regulation and cost to landlords, pushing up rents. It said local authorities already had strong and effective powers to deal with poor quality and unsafe accommodation.

Buck said she was pleased to have government backing “but I hope this will also mean finding time [in the parliamentary schedule] so we can get these measures passed into law as quickly as possible”.

Buck’s bill is also backed by the Residential Landlords Association, which represents private landlords.

“The minority of landlords renting such homes are bringing the sector into disrepute and should be rooted out of the market for good,” said Alan Ward, its chairman. “The cases raised in the Guardian show housing that is clearly not meeting the legal requirements.

“The question is what the councils are doing to take enforcement action against the landlords concerned. In the end the problem is not about a lack of powers. What is needed is a smarter system that frees up councils to better use their resources to root out the criminals”.