For the Alfajet it would not be hugely different from the Hawk. For a Hunter some costs may be higher - spares - and others lower - servicing by enthusiasts.
For UK Military aircraft there is actually a price list. As an example a Nimrod mk 1 back in the 70s was about £2,900 ph to a Government agency, say MAAF, and about £6,900 ph to a non-Governmental agency, eg a film unit.
If the private hire was perceived to have a significant
PR benefit the cost might have been reduced or waived. You only have to ask the MOD.