London Fire Brigade issued the warning on Wednesday after dozens of firefighters tackled the fire last week.
Emergency services fear the number of deliberate fires could rise in the next few weeks after a blaze in west London which is thought to have been set on purpose.
No injuries were reported and no homes were destroyed but about six hectares of land was alight, including standing crop, a field, parkland, grassland, a cemetery and an animal sanctuary.
In a statement, LBF revealed that firefighters believe the blaze was started deliberately.
It said crews have already attended more than 425 grass and open land fires across London this year.
The brigade said it is concerned that the number of deliberate grass fires could spike further over the summer holidays, particularly in light of the Met Office issuing an amber weather warning for extreme heat in London this week as the hot weather makes the ground tinder dry.
This is despite a long-term trend of deliberate fire setting decreasing by 90% since 2001, the brigade said.
Charlie Pugsley, LFB’s assistant commissioner for fire safety, said: “The reduction in deliberate fires is a testament to the hard work of our education and fire safety teams who have a long-standing history of delivering a number of children and youth engagement, intervention and education schemes in order to reduce fire risk and raise awareness of fire safety.
“However, we are still seeing too many fires being started deliberately.
“The last few years have certainly shown us how important our parks and green spaces are, with many of us spending more time than ever outdoors with friends and loved ones, so we need Londoners to help look after them.
“Whilst the dry and sunny spells of weather will be great for families looking to spend time outside over the summer holidays, it also means that the risk of grass fires is going to increase as the ground becomes drier.”
He advised parents to talk to their children about the dangers of playing with fire, to keep matches and lighters out of sight and to get in touch with the Firesetters Intervention Scheme if they have concerns about a child setting fires.
The LFB warned that grass fires can also start through barbecues and littered glass bottles.
Fire commissioner Andy Roe has written to local authorities asking for a temporary ban on barbecues in all public parks and open spaces.
The LFB said it also wants to work with retailers to stop the sale of these items to reduce the risk of grass fires.
Last month, the brigade declared a major incident in the capital as several large fires broke out in one day in areas like Wennington and Upminster, east London, and Southgate, north London.
The UK is now braced for days of extreme temperatures in the latest heatwave, as millions more people face a hosepipe ban in the coming weeks.
The Met Office has issued a four-day amber warning for extreme heat in parts of England and Wales from Thursday to Sunday, with temperatures set to climb to 35C or 36C in some places.
The vulnerable are likely to experience adverse health effects and the wider population could also be affected, delays to travel are possible and there is an increased risk of water accidents and fires as more people head to tourist spots.