Police were called at approximately 1.41pm to New Park Road to reports of a stabbing. Staff from the store came out and tried to help stop the bleeding with paper rolls of tissue.
Police gave emergency first aid to the man before the arrival of Paramedics from the London ambulance service.
Officers attended and found a male, believed to be 25, with multiple stab wounds.
He has been taken to hospital where his injuries are not believed to be life-threatening.
No arrests have been made and enquiries are ongoing.
Anyone witnesses or anyone with information is asked to call police on 101 quoting CAD 3436 or anonymously to Crimestoppers on 0800 555 111.