Valerie Clitheroe said her husband Conrad, 53, and his friend Gary Cooper, 45, are being held with their former work colleague, Neil Munro, who lives and works in the UAE.
She said they were taking notes of plane numbers at Fujairah airport, in the Gulf emirate of Fujairah about 100 kilometres east of Dubai, on February 21 when they were arrested.
The Foreign Office in London confirmed the arrests in a brief statement.
"We can confirm the arrest of three British nationals in Dubai on 22 February. We are providing consular assistance at this time," it said.
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"I'm very concerned that it has dragged on this long, we're in our 10th day now and we haven't had any information."
Cooper's son, Adam, told the same programme that the three men had already had a hearing and the authorities were in the process of transferring the case to the capital Abu Dhabi.
"They were originally arrested on the suspicion that they were taking photographs, and also for the recording of registrations (of planes)," he said.
"But now we've been told that it's been escalated from that to a national security issue."
Valerie Clitheroe, from near Manchester in northwest England, said her husband had high blood pressure and a heart murmur, and his medication would have run out by now.