One in 10 - the equivalent of more than 900,000 people - said their landlord or letting agent had failed to ensure a gas safety check was carried out in their home in the last year, a study of more than 4,300 private renters in England by the two organisations found.
An annual gas safety check and certificate is required by law and is the legal responsibility of the landlord.
The checks are designed to pick up a range of problems such as faulty boilers, and help to prevent gas leaks, explosions and carbon monoxide poisoning.
However, a separate survey of landlords by Shelter and British Gas found that one in seven (15%) was unaware of the responsibility.
Shelter chief executive Campbell Robb said: "It's shocking to think that in thousands of households across the country there are accidents waiting to happen because a simple safety check has not taken place. For households with children, this is an even bigger concern. Renters have a right to know that the property they are living in is safe.
YouGov polled 4,327 adults online living in the private rented sector in England in November and December.