The Dogs Trust suggests getting a dog reference from previous landlords
Landlords are in the dog-house with a charity which claims that three in four do not allow pets into properties.
Growing demand for rented homes has led to a rise in the numbers of pets being abandoned or handed over to charities to re-home, said the Dogs Trust.
The charity wants landlords to be more open to allowing tenants to keep dogs.
The Association of Residential Letting Agents (Arla) said it was "broadly supportive" of the Trust but it would struggle to change attitudes.
"Pet owners who need to rent privately are being forced to live in unsuitable properties, or rent with their pets without consent from their landlord," said Dogs Trust chief executive Clarissa Baldwin.
Staff at the Dogs Trust in Leeds said the waiting list had grown from 75 to 640 in six months.
They highlighted the cost of keeping a dog when household spending was being tightened.
The charity also said that housing issues were among the main reasons why dogs were handed in, alongside pets' behavioural problems.
Dogs are banned from many rental properties, the group says
The charity claimed one couple, living in the Outer Hebrides, had to move islands to find somewhere to live with their Border Collies.
In the survey of 1,400 pet owners by the Dogs Trust, nearly eight in ten said they had difficulty finding accommodation that allowed pets.
The charity is now launching a campaign to encourage landlords to accept pets and is offering tips to tenants, such as getting a pet reference from former landlords.
Malcolm Harrison, spokesman for Arla, said some landlords had their hands tied by rules that banned pets from entire developments.
Others were reluctant to allow animals in their properties owing to cleaning costs, and consideration of allergies that subsequent tenants might suffer.
He added that the group was broadly supportive of the charity's stance, but it would struggle to change attitudes during a period of high demand.
The rental sector usually sees rising demand as house prices fall, with potential homeowners delaying their move into the market.