Rebecca Brown is based in London and is the general manager of theatre company Specifiq and regularly uses BorrowMyDoggy. Since June, she and the company's artistic director, Oscar Blustin, have been looking after Wally, a Shih Tzu/Yorkshire Terrier cross-breed, once a week.
"Wally spends the day with us and after a play in the park comes to keep us company in the office," Brown told CNBC in an email. "We joined the site to spend time with a dog. With our busy (and unpredictable schedules) it is tough for either of us to have a dog, but this way we get some canine love without too much commitment.
Her experience is typical of those who are driving the demand for pet sharing services: young people, often professionals, who don't have the time or money to own a dog full-time, or need someone to regularly look after their pet.
"Everyone we have spoken to gets very excited about the idea of Borrow My Doggy and often have plenty of questions," Brown added.
"We work in the arts, and I think there are plenty of people in this industry who would love to own a pet but don't have the time or financial freedom to commit full time."
BorrowMyDoggy, which claims to have a community of more than 250,000 users, launched a crowdfunding campaign on Crowdcube this week offering equity to private investors. It valued itself at around £5.5 million ($8.6 million). The site uses a subscription model to generate revenue. Owners and borrows pay a yearly fee to the website, but users will look after someone's pet for free.
Read More Pets can be fun—especially when you rent them
Meanwhile, in the U.S., services such as Rover and DogVacay provide cheaper and more personal alternatives to kennels for dog owners by connecting them to dog-sitters in their local community. To create trust within the network, the owners and sitters are encouraged to meet in advance and users leave reviews and ratings of each other.
DogVacay launched in 2013 and says it has a community of 20,000 sitters, while its larger rival Rover launched in 2011 and claims to have network of more than 40,000 sitters across 10,000 cities. In March, Rover announced it had raised $25 million of investment from firms such as Technology Crossover Ventures and Petco to grow its business.
"Forty-one percent of pet parents have forgone a trip due to concerns about pet care," said Aaron Easterly, CEO of Rover.com, in a press release this year. "When creating Rover, we set out to provide a convenient, affordable solution that eliminates one of the most common barriers to pet ownership–lack of boarding options—so everyone can enjoy that love and companionship."
Read More Start-up DogVacay tackles $11 billion market
The demand for pet sharing services is broad. CNBC asked Eric Husk, the founder of City Dog Share, a free, non-profit organisation based in the U.S. with a network of 3,500 sitters and pet owners across the West Coast, what kinds of people want to pet share.
"A variety of people use the program. Parents with kids who don't have as much time for their dogs anymore, as well as parents with kids who host sleepovers at their house and bring a couple dogs along for play," Husk told CNBC in an email. "College kids who don't have time to walk them between classes, and college kids who miss their family dogs."
"The thing people like about our program is that we are solving a problem that they already have. We offer a free service, and people like that we are a nonprofit too."