So, these things happen (accidental boomers) and yes the Hawk can do it but you need to try quite hard!
When I did AFT on the Hawk it was part of night flying, I had completed my ‘ME lead-in’ cse by that point so didn’t get to break M1...
During one of the earlier sorties looking at transonic handling I was enjoying the cobblestones & the tail wagging when my QFI told me to slow down, we were at M0.99 & overland. We were at max chat & in a shallow dive so I can’t imagine it would have taken much more to ‘break the sound barrier’.
It would be another 30 years before I did get to finally break it, in a Typhoon.