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."
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Conservative associations in crucial marginal seats including Richmond Park and Brentford & Isleworth are meeting to select candidates.
A total of 1.7 million attacks were carried out against more than 650,000 victims of which just over 52,000 were in the UK.
The men were using ropes to lever the sofa up to the first floor apartment because it was too large to fit through the doors.