More than 90,000 people signed a petition to get Greenwich Council to agree to the memorial after initial plans were refused by the borough.
But a new campaign was launched after the council unveiled plans to add Fusilier Rigby’s name to a scroll dedicated to servicemen and women with a connection to Woolwich inside the town hall and a memorial stone inside St George’s Chapel opposite the barracks where he served.
Campaigners say it is a far cry from what the family want and have now launched a new petition.
A letter from the Rigby said: “As a family, we totally understand that it is important to have an appropriate memorial for lee and in the right place and we would be privileged to have the chance to be involved in any consultations with regard to the type of memorial being considered.”
Greenwich Council said: “The Council has held discussions with individual members of his family and the Army to ensure that their views have guided the proposals.
“The discussions centred on a memorial stone, rather than a plaque, in St George's Chapel opposite the Woolwich barracks where Lee served.
“We appreciate that other people may have views on how Lee is best remembered.
“Our guiding principle throughout has been to recognise that behind the many opinions, there remains a family grieving for a loved one taken in such shockingly tragic circumstances.”