Southwark Council has said it will look into how it can keep its parks open following calls from an MP to allow people without gardens to be given access.
Harriet Harman has suggested councils set up a rota system to allow people to use parks for exercise and fresh air.
Peter John, leader of Southwark Council, said: “We will explore all possible options so that we can keep our parks available to everyone but we need residents to keep their distance wherever they can.
"I’m calling on our residents to do the right thing and think of others - not just those who we need to protect with social distancing, but also those who have no gardens or outdoor space.
"We already have police and council wardens out this weekend, patrolling our parks, and if everyone plays by the rules we can keep them open for all, especially those who need them most.”
Southwark has 24 open spaces including Nunhead Cemetery which has been closed following abuse of social distancing measures on Saturday.
Lambeth Council has closed Brockwell Park today after people were seen by police not observing social distancing rules.