IIRC the Hawk was the last design supervised (at the early stages at least) by Sir Sydney Camm, probably the greatest designer of fighter aircraft EVER. This is not to overlook the genius of RJ Mitchell, but Camm started with the Hart, led the change to monoplanes, retracting gear, etc, then went on to Jets.
It may be old but (to an outsider anyway) it's a masterpiece.

Oldest
 

You excluded the BBMF, but not the RNHF, so how about Swordfish W5856, built 1941 and still on charge and flying in 2007.

Edit: I have just been told that W5856 is currently grounded at Yeovilton and has been for some time. Doh! Check before posting next time , PW.