They have released an image of a man they need to trace.
Det Chief Insp Garth Hall, leading the investigation, said: “We are very concerned about these attacks, which have left four men with significant injuries.
“It is clear we need to catch the man responsible as soon as possible. I would urge anyone who recognises the man pictured to contact police immediately.
“I understand there will be concern in the community about these incidents and so we have increased resources and patrols in the Hayes area to provide reassurance.”
In each incident, the suspect is described as a black man.
The first took place in Glencoe Road at about 9.30am on Wednesday, July 3.
A man of around 35 and of muscular build, with straight dark hair, attacked a 42-year-old man with a knife. causing injury to the victim’s ear.
On Sunday, July 7 there were two incidents. The first was also in Glencoe Road at around 10am.
A suspect seen armed with a knife, and wearing a hoodie and white gloves, attacked a 41-year-old man near a bus stop, causing multiple cuts to the face and neck.
The second incident that day happened around 10pm in Friar Road. A man wearing a hoodie, white T-shirt and dark trousers slashed a 57-year-old man in the face with a knife.
Then, on Monday (8) at about 3.10am, a 47-year-old man was attacked in Yeading Lane by a suspect wearing black clothing and a puffer jacket, causing injury to the victim’s eye.
Anyone with information about these incidents or who recognises the man pictured is asked to call police on 101, quoting CAD 2585/03Jul.
Alternatively, you can contact the independent charity Crimestoppers anonymously on 0800 555 111 or visit crimestoppers-uk.org