Yes, remove the hardboard and ply with 12mm ( 25mm screws I believe ) prime the ply and then use single part flex adhesive 🙂 If you left hardboard down and plyed over, the floor would be raised quite a alot...Any doors going to be affected by putting the floor down? i.e. any need shearing down? Also, any white units going to become 'lodged' in after tiling? You probably already aware of this, just thought I'd mention it.