Are there yellow signs with the heading "DEFENCE AREA" on the fence? If so, they usually list at the bottom who the contact authority is for the area.
If not, it might be worth contacting Burnham military camp given they're the closest RF presence who might be able to provide more information. Depending on what the training area was used for, there is the possibility of unexploded ordnance.
Edit: Everyone else's beaten me to it.
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