Tech start-up PetsScore, which conducted the research, said more and more tenants are now lying to landlords as a result after finding only 7% accept animals.
Around 3.2 million more pets were bought by households during the pandemic and the company is urging landlords to offer more flexibility.
The company also warned that some families are simply giving up pet ownership so as not to fall foul of landlord contracts, with a 35% increase in calls to the Dogs Trust recently reported.
PetsScore said it is urging landlords and tenants to sign up to its platform, which offers pet references to provide peace of mind.
According to the Dogs Trust, demand for puppies soared during lockdown, with Google searches for “buy a puppy” increasing by 166%.