Council tenants in east London have launched a legal action to stop the Ministry of Defence stationing surface-to-air missiles on the roof of their tower block during the Olympics.

Solicitors instructed by the residents' association at the Fred Wigg Tower in Leytonstone have formally lodged objections to plans for the missile battery to be staffed 24 hours a day while the flats are subject to armed police patrols.

The association is seeking an injunction preventing the ground-based air defence system being deployed above the heads of families living in the block's 117 flats.

Lawyers from Howe & Co are also applying for judicial review of the plan – which ministers have not yet authorised – on the grounds that the residents' human rights have been breached because they were not consulted about the proposals.

The MoD has submitted advice on how to deploy anti-aircraft weapons across six sites in the capital if there is a security scare during the Games.

Martin Howe, the firm's senior partner, said the application for a temporary injunction and for permission to seek judicial review could be considered by a judge soon. "The papers are lodged and this needs to get in front of a judge as quickly as possible," he said at the Royal Courts of Justice in London. "There are men and women who are very, very afraid."

The block, home to hundreds of children, suffered damage in a fire last December, said Howe. "Residents had to be evacuated and it was a fearful experience. The last thing they need again is the risk of an explosion or disaster at their block."

The tenants' lawyers are arguing that there has been no "fair and proper consultation process" and that the MoD is breaching article 8 and article 1 of protocol 1 of the European convention on human rights, which protect an individual's right to private life and peaceful enjoyment of their home.

They want the MoD to be prohibited from using the block until there has been a proper consultation process and an equality impact assessment (EIA) carried out which takes into account the needs of disabled residents.

Howe said: "It is incredible that the MoD think it acceptable to present women, children and men living in a block of flats in a densely populated residential area of east London with the fait accompli of having a live, high-explosive missile salvo above their heads whilst they go about their daily chores and whilst they sleep at night.

"Security of the Olympics is, of course, extremely important but could the MoD not find any other way of protecting the Olympic village than by putting the lives of hundreds of innocent council tenants at risk by turning their homes into a military battlefield position? The MoD has had seven years to work out its security plans and it needs to rethink this issue swiftly."

The other potential sites are Lexington Building in Tower Hamlets, east London; Blackheath Common and Oxleas Wood, both in south-east London; William Girling Reservoir in the Lea Valley reservoir chain in Enfield; and Barn Hill at Netherhouse Farm in Epping Forest.

The MoD said: "We are aware of the legal action following arrangements the MoD has taken up with the local landowners.

"The safety of the London Games is paramount and, working alongside the police, the MoD has been involved in a range of community engagements in these areas where ground-based air defence may be sited.

"This has involved meeting local communities, briefings and meetings with local MPs. Events have also been held to show residents the equipment and enable them to speak to [the soldiers who operate the missiles]."

In an interview with the Muslim News, David Anderson QC, the independent reviewer of terrorist legislation, said he had questioned the government about what powers were being used to put the missiles on the rooftops.

"I am watching like a hawk," he said. "We have a lot of people in intelligence agencies manning their desks, again their leave cancelled and no doubt there will be a temptation for people to use that time as the Olympics become closer to arrest people. There is a possibility that people will get worried and they will resort to power of arrest."