Therapeutic animals that give owners emotional support should get the same legal rights as guide dogs, campaigners have said.
The idea has taken off after celebrities including James Middleton praised pets for aiding their recovery from bouts of anxiety and depression.
In America, any creature can qualify as an "emotional support animal" (ESA) if a doctor says it is vital for their human companion's wellbeing.
French bulldogs, pitbulls, pigs, hamsters and peacocks have been granted the special status, which means they can go on some flights and stay in housing where animals are not usually allowed.
Now, ministers have been urged to give ESAs the same rights in Britain, with nearly 13,000 signing a petition in support of the move.
The organisers of the Change.org campaign wrote: "Sadly, unlike in America, Emotional Support Animals are still not recognised as a certified assistance animals in the UK.
"This means that the rules that apply to other assistance animals, such as guide dogs, do not apply to emotional support pets.
"This means the pet could be taken away from them, not allowed in housing etc... this list goes on.
"At the end of the day, they could be separated from their pet, which would severely impact on their quality of life and emotional well-being."
In the UK, assistance animals that are "trained to perform specific tasks" to improve their owners' quality of life are given rights under The Equality Act 2010.
This means a certified assistance animal, such as a guide dog, is allowed to accompany its client, owner, or partner, at all times and in all places.
UK airlines allow assistance animals to fly with their owners for free and they can travel in taxis and enter buildings where animals are normally prohibited.
For a dog to qualify for these benefits in the UK, it must be trained and certified through Assistance Dogs International or the International Guide Dog Foundation.
ESAs are not considered assistance animals in the UK because they are not trained to perform specific tasks.
They are not allowed onto flights by any UK airline, and any business can refuse them entry or ask owners to leave the premises.
Supporters of the online petition said their pets had helped them to survive through struggles with mental illnesses including agoraphobia, severe anxiety, depression and PTSD.
A recent study in the peer-reviewed journal BMC Psychiatry suggested that owning an animal can help relieve stress and boost positive emotions.
In September, Middleton, 32, said the "unconditional love" he received from his nine dogs - a Golden Retriever, a black Labrador, two Cocker Spaniels, and five black Spaniels - “played a vital role in my recovery from clinical depression”.
The late Star Wars actress Carrie Fisher registered her French Bulldog Gary as an ESA in America, while pop singer Ariana Grande says her pig, called Piggie Smallz, helps her to deal with anxiety.
A group called The Emotional Support Animal Registry is campaigning for ESAs to get legal recognition in Britain so flights from the UK would have to allow them on board.
Critics have said the US system has been abused, with America's United Airlines receiving 76,000 requests for support pets to board flights last year.
The company has cracked down on ESAs this year, saying only "clean and well-behaved" cats, dogs and trained miniature horses could be brought onto flights if their owners have a doctor's note.