Plans for cars to use part of a park under the M4 flyover have sparked fury among users of the site.
The broadcaster wants the parking spaces under the motorway to be available for contractors five days a week until December 23 this year.
It says cars would enter via the road to the existing car park, off Boston Manor Road, and only a permeable temporary cover would be needed to avoid any permanent damage to the grounds.
However, the application, received by Hounslow Council on April 9, has not gone down well with supporters of the park.
Linda Massey, of the Friends of Boston Manor, said: "We don't want the park to become a glorified car park. If this is allowed to happen it will set a precedent for the future.
"We already told GlaxoSmithKline years ago we didn't want cars parking here. It's bad enough having commuters using the organised car park here.
"As one of our trustees recently said there are quite a few underused car parks in the area which could be used instead."