Assistant Chief Fire Officer Simon Moore said Mr Cox was not on a call at the time.
He added: "The circumstances of his death have not been established. We are saddened and upset by this tragic news and our thoughts are with his family and colleagues at this very difficult time."
Mr Cox, 53, who was known as "Biff", died at around 6pm after collapsing at the fire station, the Surrey branch of the Fire Brigades Union said.Colleagues tried to resuscitate him but were unable to save him.Richard Jones, the brigade branch secretary, said:
Fire Services, charities and individuals from the service across the country have sent messages of condolence to Surrey Fire and Rescue after the death of a firefighter at Staines.
Clifford Cox died at Staines fire station last night, Surrey Fire and Rescue Service said. His next of kin and family have been informed.
Chief fire officer Russell Pearson said Mr Cox was part of the station's Green Watch, and had served as a firefighter in Surrey for nearly 25 years.
Surrey Fire and Rescue have confirmed the death of a firefighter who was on duty at Staines fire station.
Next of kin have been informed.
Ria Chatterjee is in Staines, where homes are being evacuated and water levels are still rising.
More heavy rain is expected over the next few days.
Residents in Staines were woken by telephone flood alerts today as the River Thames submerged a footpath and began to move towards homes on Laleham Road.
There are problems on the M3 in Surrey. Three lanes are closed due to an accident on the London bound carriageway between J2 M25 and J1 A316 (Sunbury / Staines). It's expected to cause long delays.
The departure board at Staines railway station this morning showed delays on every single train into Waterloo.