DC10,
Nope; it's there in black & white. If not a Qualified Service Pilot (QSP) then an ATPL is required. I think there are still one or two non-QSP AEF pilots out in the sticks who have PPL or CPL but they will have 'grandfather rights'. All new non-QSP, AEF pilots need an ATPL. Even then, I suggest that it's not an automatic right of entry.
I suggest that perhaps it's not entirely the fault of the RAF, remember that the waiver to fly a public transport category aircraft (which the Tutor is, given its role) without a licence only applies to QSP (Rule 58? of the ANO).