The incident in Hampton Court, in south west London, was filmed by cycling instructor David Williams, 47, who recorded it on his helmet camera and posted it on YouTube.
The female driver was behind the wheel of a red Land Rover Discovery.
Surrey Police said their enquiries were "ongoing" into whether a crime had been committed.
Mr Williams said: "It is disturbing that people think driving while eating a bowl of cereal is acceptable.
"She was coming up to a junction - it is incredible a person in such a large vehicle can consider that is a good way of conducting themselves on a road."
He also told the Evening Standard he thought the bowl contained "porridge or muesli".
In a statement, Surrey Police said: "Enquiries are ongoing and we are in the process of obtaining the footage online so that further enquiries can be carried out to establish whether any offences have been committed."
Under Crown Prosecution Service guidelines the offence of driving without due care and attention under section three of the Road Traffic Act 1988 is committed when a person's driving "falls below the standard expected of a competent and careful driver".
A driver caught on camera eating a bowl of cereal is being investigated by police.