Objectors have sparked controversy by demanding a memorial honouring a Polish activist killed in the July 2005 bombings be moved.
Hammersmith and Fulham Council granted planning permission for the obelisk to be planted in Ravenscourt Park, King Street. The memorial was unveiled last month and now The Hammersmith Society is now calling for it to be moved.
Chairman Angela Clarke from Standish Road, Hammersmith, said: "It is in a totally inappropriate part of the park and we will do all we can to try and persuade the council to move it to an alternative location. We've had a lot of comments from members saying why on earth has the council put that awful thing in the middle of the park?"
The cenotaph commemorates Giles Hart, 55, who ran the Polish Solidarity Campaign, which helped topple communism in Eastern Europe, from the Polish Centre in King Street, Hammersmith.
Mrs Clarke added: "Now the council has opened the floodgates to anybody who fancies putting up a memorial in the park.
"Having granted planning permission for this one, the council has set a precedent and they might find it hard to refuse others."
Wiktor Moszczynski is chairman of the Giles Hart Solidarity memorial committee which campaigned for the memorial.
He said: "There has been such an emotional investment in this. This campaign to churn up the stone and implant it shamefully out of sight somewhere else sounds fairly heartless to me. All new monuments, including modest-sized ones like the Giles Hart Solidarity
Memorial, need time for residents and park-users to adjust to their presence and I would humbly urge the activists of the Hammersmith Society to allow the people of Hammersmith the time and opportunity to make that adjustment."
The four-foot high granite memorial is inscribed in English and Polish: 'A lifelong campaigner for freedom and human rights honoured by Solidarnosc (Solidarity) as one who supported Poland in her hour of need.'
A H&F Council spokesman said: "We think that the memorial does not detract from the park and is a welcome addition."