I saw a poor (American) guy a LHR last week who only had his laptop (without bag) and a small bag with his travel docs, passport etc.
He was given the alternative by the BAA jobsworth at flight connections to either check in his laptop (without bag) OR his travel docs bag...
BA has (or at least has had until recently) these cheapo white/tartany shopping bag things made out of woven poly that you can ask for at check in. Ostensibly they're for checking items being removed from a bag that initially weighs in too heavy, but could also be used to combine carry-on items in a pinch.