The parks police service has increased patrols of its green spaces to ensure visitors are obeying the two-metre rule.
Wandsworth officers have also put tapes and barriers around playgrounds and outdoor gyms, and are asking those having gatherings to move on.
Wandsworth town hall is getting regular complaints of people ignoring the rule in place since last week when the UK was put on coronavirus lockdown – particularly in parks and open spaces.
Some people have continued using outdoor gym equipment despite these facilities being closed off.
The behaviour of a handful of people is causing concerns that the strict measures to combat the spread of COVID-19 are being seriously undermined.
Wandsworth council leader Ravi Govindia said: “I am very grateful to the vast majority of our residents who are complying with the rules on social distancing and behaving responsibly to help prevent the spread of this deadly virus.
“However there are some who are acting as though the current health crisis is just a figment of other people’s imagination and are taking little or no notice of the medical advice to keep their distance and avoid the risk of infecting or contracting this disease.
“I have been frankly amazed that small groups of people are still gathering together in close proximity and putting their lives, and the lives of others at risk.
“Their behaviour in the midst of a pandemic is totally irresponsible.
“The police are taking action to stop this mindless behaviour so I would urge all residents and businesses to play by the rules and stay safe.
“These restrictions won’t last forever but the longer people flout the rules, the longer it will take to beat this virus.”
Government guidance states that everyone should stay at home. People should only go outside for food, health reasons, to help vulnerable people or to work – but only if you cannot work from home – and stay two metres (6ft) away from other people.
Pictured top: Tooting Bec Common