Pheobes, in Catford, south London, is set to close in the summer, after the season.
The 70-year-old company is set to continue its landscaping business but the shop site could go for development.
A representative said it was hoped the land would be sold off. She said: "It started off a flower stall back in the day and has developed over the years. I've seen lots of people come and go. It's the end of an era."
TV presenter Johnny Morris opened the pet centre at the 9,000sqft retailer in 1988.
Meanwhile, Leighton Buzzard Garden Centre in Buckinghamshire is to shut. Martin and Stuart Hammond opened the site in 1995. The centre has two full-time and 10 part-time staff. The garden centre cafe will also close but 10 other businesses including an aquatics centre, beauticians, dog groomers, a pet shop, car wash, crafts centre, hot tub and pool suppliers and installers, a conservatory company and a children’s nursery occupying rented facilities on site and employing around 40 people altogether, will continue trading.
The owners said they had received approaches to carry on the £1m-plus business but they had not been followed through and that they were open to further interest.