RAF Chivenor, was, until recently a fairly large military airfield, home to the TWU, flying Hunters and Hawks, as well as other military types operating from there, including SAR Wessex and Sea King helicopters.
During WW2, it was a Coastal Command airfield, under 19 Group, and was opened in 1940. A year or two later, to accommodate heavier aircraft, three asphalt-covered concrete runways were laid, the longest being 2,000 yards x 50 yards (this became the main post war runway, extended to around 4,000 yards), with 45 'spectacle' or loop type dispersal points, and a further five 150 feet diameter 'frying pan' dispersal points.
Staff was a total of 2,678 men of all ranks, and 333 WAAFs.
By the late 1980s, it was a very large airfield indeed, stuck out on that spit of land to the south of Braunton, where a friend of mine had a restaurant.
Approaching from the sea, RAF Chivenor would be to your right, across the Taw, and was not normally open to civilian traffic. However, at the time you visited, a far as I remember, there was a small airstrip on the opposite (left) side of the Taw, which would have been under RAF Chivenor Radar and Approach control, and perhaps this is where you landed.
I'm not totally sure, but I believe Chivenor was closed under the latest Defence cuts, with the TWU either now totally at Brawdy, or centralised at the home of all UK Hawks, at Valley, on Anglesey.
The RAF now shares its ten aircraft with the three remaining operational airfields, until next month, when funds will not allow flying on any day that has a 'Y' in it's name ......