Conservative-run Wandsworth council in south London has started eviction proceedings against a woman whose son appeared in court charged in connection with the riots in Clapham Junction.

It is the first local authority to issue an eviction notice on a tenant in the wake of the riots although Westminster, Greenwich, Hammersmith and Fulham, Nottingham and Salford councils have all said they will consider evicting those found to have taken part in the unrest.

The mother and son cannot be named for legal reasons and a judge will take the final decision about their proposed eviction. David Cameron gave his backing to the move. "I think for too long we have taken too soft an attitude to people who loot and pillage their own community. If you do that you should lose your right to housing at a subsidised rate," he said.

He dismissed the idea that the move might be counterproductive and create deeper poverty for those affected. "Obviously that will mean they will have to be housed somewhere else and they will have to find housing in the private sector and that will be tougher for them. But they should have thought about that before they started burgling," he said. "In some cases, it may help break up the criminal networks in some housing estates if some of these people are thrown out of their houses and I think quite right, too."

Wandsworth council's leader, Ravi Govindia, said that, in signing a tenancy agreement, tenants had agreed not to take part in activities that could jeopardise their housing. The council felt it had the power to terminate the agreement against the tenant, despite the fact that she was not involved in the riots and her son has only been charged, not been convicted.

"The mother can challenge the notice-seeking process," he said. "The tenancy agreement does not just apply to the mother but the entire household."

He said she would be deemed to have made herself deliberately homeless. "Then our obligation would be at an end. She signed the contract in which she and her household would agree the terms of the contract."

Govindia said he hoped the move would dissuade others from taking part in civil unrest. "People in society do know what lines they should not cross, and if you ignore the fact they have crossed the line it only encourages people to cross the line regularly," he said.

Stephen Howlett, chief executive of the Peabody Trust, one of London's largest housing associations, which runs the Pembury estate – next to some of the worst violence in Hackney, north London, on Monday – said he thought courts were likely to find eviction of tenants caught up in the riots disproportionate. "We want the strongest action to be taken against those involved, but our preference is for the criminal justice system to be the focus."

He added that the measures risked simply moving the problem to another area, or pushing tenants further into poverty. "These people have to live somewhere, so if they are evicted you risk just exporting the problem."

He had talked to a mother on the Pembury estate who was was "terrified that she and her younger child would be made homeless as a result of her 17-year-old who she could not keep under control". He added: "This is not simple. We have to be very careful."