The BBC reports that 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 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.
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.
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