Thanks for the reply.
Yes, I'm semi-detached (as is my house)
The chimneys back on to each other. So how does it work if it's a downdraft? the emmissions from my gas fire are going up my chimney and down my neighbours? Didn't realise that could happen. Okay, I think I'll try the cowl thing first - thanks for that advice. The neighbour is being rather snippy about it so it's a bit tricky. Don't want them to have a gas residue smell obviously, but there isn't a lot of proof that it's coming from us. Apparently no-one else can smell it, and they haven't gotten an expert to check if there are emissions, so we're being asked to go to all this expense, just on their say-so.
Also, does anyone know if chimney experts can check if your chimney needs to be lined? I guess there's a way to prove our chimney is worn out?