Officers believe that George and Jean Mowlam, aged 89 and 85 respectively, were targeted because their garden in a street off Mulgrave Road was so overgrown it hid their property.
PC Rob Davie, who organised the clear-up, said: "When I visited this couple after they had been burgled I felt so sad and wanted to do something to help them especially as they have no immediate family and the distant relatives they do have live a long way away.
"It felt like it was the right thing to do and it will go a long way to improving their security by improving the visibility of the property as well as their quality of life by bringing a lot more light into their front kitchen and living room where they spend much of their time."
Retired Sutton police inspector Stuart Hooper-Hinks, who now runs Absolute A1 tree and hedge services, came along to support the officers and provide all the heavy equipment like chain saws.
"Cutting back the garden will make a phenomenal difference to the couple. All you could see from the street before was part of the garage door. Now the whole property can be seen clearly."
George, who used to be a BBC engineer and was involved in the launch of Radio, 1, 2, 3 and 4 all on the same day in 1967, commented: "It's been growing for several years and it's a job that needed doing.
"It was a great surprise when the police told us that they would be happy to clear our garden - and it's very good of them - and finally it's been done."
Sutton Council supported the clear up by providing extra rubbish bins.
The couple were burgled on Sunday, 15 November when a small quantity of cash and other items were stolen.
Caption: George Mowlam; retired police inspector Stuart Hooper-Hinks; and PC Rob Davie