Chimneys are meant to 'draw', so should be sucking air out of the living room and up the chimney, not the other way round.
But there are circumstances when the flow may reverse. In my old house, the draw on one chimney from a live fire was enough to draw air down another upstairs chimney.
In the neighbour's property, who knows what might be reversing the air flow. It might be a natural occurrence of some kind due to the building's layout, or an unnatural cause like bathroom fans and extractors over hobs.
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thanks all.
Enjoy your fire :-)