The AELTC’s proposals were given planning permission in 2024 and would see the existing site nearly triple in size.
The club said it only planned to build on private land it had previously purchased at the former Wimbledon Park golf course in south-west London.
However, SWP believe the public Wimbledon Park is at threat.
Speaking to BBC London, SWP member Susan Cusack said: “I think that what the All England Club want to do is just far too large.
“Our concerns are digging up 73 acres of metropolitan open land, the ecological and environmental damage that will do, [and] the issue that it will have with all the locals for 10 years while they’re doing all that building work.”
The AELTC wants to expand the site so it can host qualifying matches, in line with other Grand Slam tournaments.
But Cusack said she did not believe such a large development was necessary for the Wimbledon Championships.
“You start off with 128 people on day one. On day two, you have 64.
“So, probably, you don’t quite need 38 courts, a stadium, a maintenance building …. and nine other buildings on metropolitan open land.
“This is corporate greed and it’s corporate hoarding,” Cusack said.