Update 2...
Ok, the frame is back from Argos with the sleeve inserted. However, looking at the bb shell, I notice that on one side, the remaining 'shell' on the frame is an even thickness of metal all the way round the circumference with the sleeve centrally inserted, while on the other side of the frame, there's a lot more thickness to the metal at the bottom of the bb shell than at the top.
I'd expected the reaming to go exactly through the middle of the bb shell, leaving an even thickness of metal all round the rim of the bb on both sides of the frame, and this suggests that it hasn't. What concerns me is, if the reaming isn't straight and the new sleeve isn't in straight, then the bb won't go in straight and the cranks/chain will be tilted when installed. Also, surely if the remaining metal at the top of the bb is substantially thinner than at the bottom, there's going to be a weakness there?
Needless to say I've left word for Argos to contact me to discuss it before I start rebuilding...
Watch this space.