As a student, and QFI, on the Hawk spinning was part of the syllabus.....I seem to recall some instability in the spin, and one of the recovery criteria was excessive side forces, suggesting as others allude to that it was reluctant to spin anyway. Centralising always worked.
I got the impression that the Hawk 'spin' was just really a stall with rudder induced yaw. Centralising the rudder (easy due to the forces) just ended up with a stall. A very benign aircraft.