thisflys over the existing ceiling joists (which hold up a bonnet roof
over the bay window). The main floor joists are then hung below this
beam on long hangers. I presume similar could be done even if the floor
joists are SHS rather than timber.

Yes, that looks similar to my proposed solution, although on a grander scale
and with the stairs in a different location.

Has anyone got a definitive answer as to whether the steel joists can be
"hung" off the structural beam and how?

Christian.