An announcement from the charity’s head office confirmed the closure of the outlet in Richmond Road, Twickenham, with the store due to close on October 26.
Customers have expressed shock at the sudden announcement, with one employee understood to be affected.
Martina Gomez, a mother and frequent customer, said: “A lot of people will be sad to see the shop go – all the animal welfare groups are upset by this decision.
“I am the parent of a young man with autism that goes to the shop twice a month for books.
“He for one is upset the shop is closing, as are the missing local pets, homeless and lonely residents who pop in for a chat and members from my Facebook group have been emailing their concerns to me.
She said the manager of the shop went “above and beyond” to help her autistic son.
The RSPCA confirmed that it would be closing some of its centrally run stores which meant that it would also be making some redundancies as a result of a decline in high street shops.
A spokesperson for the RSPCA said: “A review of a small number of charity shops run by the national RSPCA was recently undertaken to determine whether it made financial and commercial sense for the national Society to maintain such a small retail network.
“Unfortunately, several charity shops run by the Society were no longer profitable so, in this challenging financial climate, we had to make a difficult decision on their future.
“The Richmond shop is one that will be closing, and the shop’s final day of trading will be October 26th.
“We are so grateful to people who have given their valuable time to help animals and we are hoping to explore new ways they can help the RSPCA if they would like to continue.
“These closures do not affect the more than 300 RSPCA branch-run charity shops, which raise much needed funds for local animals in need.”