Epilogue:
Despite the gas to the whole building being entirely disconnected, both my CO alarm and my downstairs neighbour's went off at 7.30 this morning. Called the people out again who confirmed that this must mean the CO is coming from somewhere else. Turns out the timing was significant - 7.30 is when next door's central heating goes on of a morning! Their flue points in the direction of our building and their boiler was leaking. The CO was actually climbing up the wall and coming into our flats! Ironically, opening all of the windows last night made it worse, and also the reason that the levels didn't start to drop until 11pm - when next door's heating switches off.
So, we all had a freezing cold night - not, I suppose, the end of the world in the general scheme of things. The gas people have been back and reconnected all of our supplies and all is well again.
Once again, if you don't have a carbon monoxide detector, get one now. And check it every week.