The joint DfT and military project team is the same SAR(H) team that sorted out the recent bidding and award process for the interim contract given to CHC.
The MOD has firmly backed continued military presence in UK SAR so the probable outcome is COMR (Civilian Owned Military Registered) to allow this to happen.
I suspect the aircraft will have an MCA corporate paint scheme but you will have pilots from RAF, RN and MCA flying them.