"It is also the case that animals may act as fomites, as the virus could be on their fur in the same way it is on other surfaces, such as tables and doorknobs. That's why good hand hygiene remains important."
Several dogs, cats, tigers, lions and mink have contracted coronavirus globally during the pandemic but all are thought to have picked up the disease from their owners and keepers.
Professor Margaret Hosie from the MRC-University of Glasgow Centre for Virus Research, said: "There have been sporadic reports of cats from Covid-19 households in Hong Kong, Belgium, France, Germany, Switzerland, Spain and the USA that tested positive for coronavirus and were presumed to be infected from their owners, but this is the first report of an infected cat in the UK.
"All available evidence suggests that the cat was infected from its owners, who had previously tested positive.
"The cat and its owners have since made a full recovery and there was no transmission of the virus to other animals or people in the household."
Experts said it was important for people to stay away from unknown cats and also keep their distance from their own pet if they experienced symptoms of Covid-19.
Dr Rachel Dean, Director of Clinical Research and Excellence in Practice for UK veterinary group, VetPartners, said: "If you do get sick then avoid close contact with your cat, wash your hands before and after contact, don't let them lick your face.
"If it won't harm the welfare of your cat you could consider keeping it indoors but many cats don't like that.
"Don't touch a cat that isn't yours, just as at the moment we don't shake hands or hug people we don't live with."
Prof Jonathan Ball, Professor of Molecular Virology, of the University of Nottingham, added: "The best thing you can do to protect your pets, is to avoid close contact if you are, or think you might be, infected with the virus."
The government also warned pet owners and those coming into contact with animals to wash their hands regularly.
Chief Veterinary Officer Christine Middlemiss said: "This is a very rare event with infected animals detected to date only showing mild clinical signs and recovering within a few days.
"There is no evidence to suggest that pets directly transmit the virus to humans. We will continue to monitor this situation closely and will update our guidance to pet owners should the situation change."
The British infection was spotted by scientists at the University of Glasgow who have been screening hundreds of veterinary samples to find out if Covid-19 is in the feline population.