Armed police "flooded" Sunbury Cross shopping centre after reports of a group of youths fighting on Wednesday evening.
Surrey Police were called to reports of teenagers fighting at around 5.10 pm outside Marks and Spencers.
During the fight a 19-year-old man was stabbed with a "large blade", believed to be a machete approximately 30cm long.
It was reported that the other youths fled the scene towards the nearby Spelthorne Grove estate.
The victim received first aid in a nearby shop and was taken to hospital where the injury has been described as serious, but not life threatening.
The group are described as being white and mixed race males, aged between 14 and 19, mostly wearing jogging bottoms and hoodies, all with face coverings. Some of the group are believed to have had bicycles.
Police would like to speak to anyone who was in the shopping centre between 16.45 and 17.30 on May 19.
They are particularly keen to speak to anyone who may have dashcam or helmet cam footage, or mobile phone footage, of the area that may show the people responsible.
Police believe that it is possible that a delivery driver could have captured the incident without being aware what was happening due to the amount of fast-food outlets nearby.
Sergeant David Richardson said: “We understand this will be an alarming incident for shoppers and locals, as it happened in front of many people in broad daylight.
"I would like to reassure the community that we are doing everything we can to find those responsible.
"If you have any information which could help our investigation, I urge you to please get in contact with us straightaway.”
Police say that drivers along the A308 around the same time may have captured footage, or saw the group of people responsible as they travelled to or from the location.
They are urging anyone who may spot discarded clothing or weapons in the vicinity to contact police without touching the items, so that they can be forensically recovered.
If you have any information which could help, contact police on 101 quoting incident/crime reference number P21105771.
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