Okay.......I had a quick think about this and then re-visited the scene of the crime.
The problem was a combination of a bad connection and my unfamiliarity with the computer.
I made sure that all the cable connections were well pressed together and I got the computers default background appearing on the tv..
I then dragged an icon off the computer screen and lo and behold it appeared being dragged on the tv screen.
I had an extra display! 
Found the control for "mirroring" and voila !......my computer screen!
Hi 
I have a MacAir with a mini display port.
I have purchased 2 x connectors, one for VGA and one for HDMI.
I connected to my tv using the HDMI adapter and on the 1st attempt I got the MacAirs default screen picture, but nothing else. As I did things on the computer nothing happened on the tv.
On the 2nd attempt there was nothing. The tv display says no signal.
I went to "Display Preferences" and found the "Detect display" button, but nothing happened.
Chowhound
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