Police were called at 5.30pm on Monday, 20 July to reports of an assault on Upper Green East in Mitcham.
Officers attended but there was no trace of a victim.
Police were called a short time later to a south London hospital after a man, aged in his early 30s, self-presented with stab injuries.
He remains in a critical condition.
A large crime scene is in place.
At this early stage, there have been no arrests. Enquiries continue.