While the events will held in a corner of Greenwich Park, the plan relies on the use of nearby Blackheath Common for a 26-acre operational compound which will include stables and training facilities.
The group NOGOE (No to Greenwich Olympic Equestrian Events) believes the plans to use Blackheath Common's Circus Field would be unlawful because erection of the planned compound would not be not permitted under the Metropolitan Commons Act 1866 and the Supplemental Act for Blackheath of 1871.
Retired solicitor Lionel Lewis, who researched the act, noted the reference to a management scheme for Blackheath, which he then located in the Heritage Library at Woolwich Arsenal.
"The Scheme not only prohibits enclosure generally but limits enclosure by those managing the Heath to the shortest period of time for the purpose only of repair of the grasses," the group said.
"Further research into the Commons Act of 2006 has revealed that where there is a scheme, such as at Blackheath, there is no means for obtaining any permission to build any fence or structure.
"So, if the current managers, Greenwich Council, were to give [games organisers] permission to use this land, they would be breaking the law of the land, and NOGOE would then consider legal action."
Lewis, who worked with distinguished local historian Neil Rhind and the Blackheath Society on this investigation, believes games organiser's plans cannot go ahead and is amazed they appear not to have researched these laws, despite their team of lawyers.
He is equally surprised that Greenwich Council, in entertaining an application for the use, appear to be unaware of laws relating to the land they are supposed to manage.
NOGOE co-ordinator John Hine said: "We are most impressed with the careful research that has been carried out by Lionel and Neil. They have developed what seems to be an unarguable case, which we expect the council to endorse.
"We always said that Greenwich Park was too small and since LOCOG [the London Games organising body] are unable to use Circus Field, it should do the decent thing and take the events to a venue which does have the space, but not the fantastic heritage that they wish to destroy at Greenwich."
However, Games officials have expressed confidence in their efforts to gain planning approval to use Greenwich Park and Blackheath Common.
Plans for Greenwich Park include a temporary 23,000-seat arena.