One in 10 renters in England have fire safety concerns about their home, a poll commissioned by Shelter suggests.
And 15% of tenants say problems with the state of their property are making them ill.
The housing charity is backing a private members' bill which would change the law to give renters more rights to force landlords to make sure properties are safe.
The government has told 5 live Investigates it is supporting the bill.
The survey of 2,576 private and social tenants in England found more than 250 had experienced a fire, gas leak or concerns over fire safety in their home in the last 12 months.
It also showed 380 renters had experienced physical or mental health problems because of the general poor condition of their home over the same period.
Venetia Dolphy, 34, from Bromley in London, said she and her two children were made ill after living in two housing association properties with serious damp.
She said she was also diagnosed with depression and began suffering with asthma, despite never having it before.
"The kids were constantly sick from the cold and the damp. On one occasion I had an asthma attack that I just couldn't control and spent four days in hospital," she said.
"I think it's important people understand the effects it has on people, it's just a nightmare."
The housing association has now repaired the damp in her home.
Carol Richards, 58, who has mobility problems, lives on the 17th floor of Cruddas Park tower in Newcastle.
After the Grenfell fire, which killed 71 people, campaigners in the city asked Your Homes Newcastle to install extra fire prevention measures in the block, such as smoke detectors in communal areas and air tight lids on bin chutes.
Since then, there have been two fires in Cruddas Park tower in the space of six weeks. Both broke out at night but no-one was hurt.
Campaigners say the fires could have been prevented or dealt with much quicker if the prevention measures had been put in place.
Mrs Richards said: "I have to go to bed in the day when my carer gets up because I'm petrified of going to sleep.
"If there is another fire we might not wake up and I wouldn't be able to get down the stairs."
Your Homes Newcastle said the fire service had inspected the blocks and said they were "among the safest in the country".
However, it added discussions with residents were ongoing with regards to sprinklers and other fire prevention measures.
'Catastrophic consequences'Shelter is backing Labour MP Karen Buck's private members' bill which would give tenants more rights to force landlords to ensure properties are safe, well maintained and habitable at the start of every tenancy.
The charity's chief executive, Polly Neate, said: "The Grenfell tragedy exposed the catastrophic consequences of unsafe housing in the most devastating way, and how our laws fail to protect people's right to a safe and decent home.
"Too many private and social renters are forced to live in poor and sometimes dangerous conditions, unable to tackle safety concerns or legally challenge their landlord."
Housing Secretary Sajid Javid said everyone "deserves a decent and safe place to live".
"Councils already have wide-ranging powers to crack down on the minority of landlords who rent out unsafe and substandard accommodation," he said.
"However, public safety is paramount and I am determined to do everything possible to protect tenants.
"That is why Government will support new legislation that requires all landlords to ensure properties are safe and give tenants the right to take legal action if landlords fail in their duties."
A spokesman for the Ministry of Housing Communities and Local Government said councils already have strong powers to make sure landlords make improvements, and were expected to use them.
He said the government was also introducing a raft of new powers.
"We will continue to have discussions with Ms Buck regarding her private members' bill," he added.