Ministers are being urged to ensure cats and dogs get Covid jabs once all people have been vaccinated.
Experts say vaccinating pets may help stop variants developing and spreading.
Labour ’s Sir Mark Hendrick said: “Covid possibly started in bats. The priority is to vaccinate humans, but a year or so down the line we have to look at animal vaccines.”
And Kevin Tyler, editor of journal Virulence, added: “Mutations could come back into humans looking quite different.
“A substantially different variant could be a problem in the future. The best way to deal with that might be vaccines.”
Animal-to-human transmission is rare – but last July a cat tested positive in the UK after catching the virus from its owner.
The British Veterinary Association recommends owners wash hands after touching pets in case the virus is on their fur.
Russia has developed the first animal-specific jab tested successfully on cats and dogs, and a US firm is also working on one.
Independent SAGE virologist Prof Deenan Pillay said: “It may be the current vaccines would need a tweak for nonhuman species.”
Denmark culled its 17 million mink after finding a coronavirus mutant in fur farms, and ferrets have infected cats in lab tests.
A tiger in New York’s Bronx Zoo and eight gorillas at San Diego Zoo are thought to have caught the virus from keepers.
Environment minister Victoria Prentis said there is no evidence of infected farm animals and no current plan for pet jabs.
But she added: “If the biology changes such that companion animals become important in transmission, we’ll reconsider.”
Sir Mark added: “The more we exploit the world, the more likely it is to bite us back.”