“A 30-year-old man [A] and a 31-year-old man [B] have been arrested in connection with this incident and are currently custody.
A London Ambulance Service spokesman said the men made their own way to hospital.
Meanwhile, a third shooting took place in Croydon, where a man, in his 20s, was shot.
A police spokeswoman added: “Police were called at approximately 01:40hrs on Saturday, 01 August to London Road Croydon following reports of a gunshot.
“Officers, including armed officers, and London ambulance service attended.
“A man, believed to be in his twenties, was found with a gunshot wound. He has been taken to hospital and his injuries are not believed to be life threatening.
“No arrests and enquiries continue.”