The incident took place between 12noon and 12.15pm on Thursday, 4 June when the victim, a woman in her thirties, was walking by herself down Woodham Lane.
As the woman was walking down the road a car drove past her and a man grabbed the rucksack she was carrying on her shoulder and pushed her to the ground.
The man then got into the front passenger seat of the vehicle which had just driven past and the car drove away towards New Haw.
The vehicle used in the incident is described as a black four door Peugeot which was either new or had been recently cleaned and had a green Monster energy drink sticker on rear number plate.
The stolen rucksack is dark blue with a black checked pattern and a Van Air logo on the front.
The man who grabbed the bag is described as being white, in his late teens or early twenties, tanned complexion, 5ft 8ins tall, muscular build, short blonde hair with two lines shaved into the left hand side.
He was wearing black, white and red coloured Nike Air Jordan trainers, white Adidas tracksuit bottoms and a red polo shirt. He was also wearing several large rings on his left hand.
The man driving the car is described as being white and spoke with an Irish accent.
Officers are also looking to trace a white woman with long blonde hair which was tied back in a ponytail and was wearing large hooped earrings and a pink and white top, who was sitting in the back of the car.
There was also a white and brown pitbull type dog with a brown studded collar in the car.
Detective Constable Nicola Bartholomew, who is leading the investigation, said: “This was a nasty incident where a woman who was simply minding her own business has been assaulted and robbed.
“Fortunately the victim only suffered minor cuts and bruises during the incident but she has understandably been left shocked by this cowardly attack.
“The fact that the offenders carried out this robbery in a busy area and in broad daylight shows that they were prepared to take risks to get what they wanted and such behaviour will not be tolerated in Surrey.
“I would like to hear from anyone who recognises the descriptions of any of the people seen in the car or with any information about the vehicle and where it went following the robbery.
“As part of the investigation officers are carrying house to house enquiries in the area and are in the process of reviewing local CCTV footage.
“Incidents of this nature fortunately do not take place often in Runnymede and I can assure residents that we are working closely with the local neighbourhood teams to track down those responsible.”
If you witnessed the robbery or have any information please call Surrey Police on 101, quoting reference 45150047076, or call independent charity Crimestoppers anonymously on 0800 555 111.