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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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.