I too have seen more rats than normal on Tooting Common (and to a lesser extent on Wandsworth Common). I have asked Cllr Steffi Sutters and council officers for their advice. Here it is - and a sensible and measured approach I think:
Rats are particularly attracted to the Commons as they like water (we have our lakes and lots of water on the Common at the moment), and most importantly, because so many people feed the birds and leave bread, seeds and other food it encourages them to remain.
Brown rats are actually a very important part of the decomposition process, scavenging dead and weak animals, food waste left behind by visitors, eating dog poo, and helping the ecosystem by clearing dead things and detritus. Rats themselves are predated on by birds of prey such as sparrowhawk and owls, both of which we are lucky enough to have on Wandsworth Common, so this keeps the population in some sort of balance. While people continue to feed the birds on the Common, the population of rats on the Common will remain, and the regular/increased feeding is what is causing the rats to become so bold. Tackling this is a very difficult thing to do as it seems to be a favourite past-time for so many people.
Both commons are bisected by multiple railway lines which provide fabulous wildlife corridors and provide a sanctuary for rats both from predators such as dogs and also additional ample food stuffs both natural and from food waste litter thrown over boundaries.
Nothing effective and worthwhile can be done to “control” rats because they are widespread and numerous which makes any kind of attempt to be rid of them complex, continuous and expensive but more importantly if we want to see viable biodiversity rich habitats then rats are part of that, they fulfill an important niche. All the while the food sources remain, even if we were able to reduce numbers in the short term the populations would rise again rapidly.