Officers were called to two areas of Feltham within six minutes on Thursday afternoon with three people found injured.
In a statement, the Metropolitan Police said: “On Thursday July 4 at 2.07pm police were called to Alcott Close in Feltham to reports of a stabbing.
“On police arrival officers found a male with a stab injury. The suspect was no longer on scene. The male received medical treatment.
“Six minutes later, police were called to Walsham Road to reports of a stabbing at the location.
“On arrival, officers found two males with stab injuries. The suspect was no longer on scene.”
The attacker remains at large and no arrests have been made yet, police said.
Two of the victims’ injuries were initially thought to be life-threatening but police later said all three men were in a non-life-threatening condition.
A Section 60 order, giving officers additional search powers, is in force in the area, Hounslow Police said on X.
It is currently understood the incident is not linked to terror and the Met Police said there was no link to the General Election or polling day activity.