The charity said people were rethinking owning a pet as restrictions eased across the UK.
It comes after the sale of pets in the UK increased at the start of the Covid-19 pandemic as more people spent time at home.
An estimated 3.2 million UK households welcomed a new pet into their family during lockdown, with dogs and cats being the most popular animals, according to Pet Food Manufacturers’ Association.
Owen Sharp, the charity’s chief executive, said: "Following the boom in pet ownership during the pandemic which saw millions of us delighting in the companionship of a dog, today’s figures have sadly come as no surprise to us.
"As owners’ circumstances change, puppies grow into boisterous ‘teenagers’ and the country unlocks, many owners are being forced to reconsider the place in their lives for their pet."
The charity called it a “looming crisis” and expect the number of dogs it receives in the coming months to increase.
These concerns were echoed by The Kennel Club, which warned the UK was facing a looming “welfare crisis for pandemic pups” unless more workplaces become dog friendly as more people return to offices.
Bill Lambert from The Kennel Club said: “This new research worryingly shows that if dogs can’t go to places with their owners, and fit their lifestyle post-pandemic, some will be left home alone for too long, or even sadly rehomed or abandoned.
“These consequences could be quite devastating for the nation’s dogs, who frankly don’t deserve to be left behind after being a lifeline for so many during lockdown.”
He added: “Hospitality, businesses and workplaces can play a role in combatting the looming welfare crisis faced by this pandemic pup generation by being open for dogs; helping owners to introduce or re-introduce their pet to ‘normal’, without leaving them behind.”