isn't the boiler a gas leak hazard ????? hasn't your mouth/lips been feeling a bit dry of late until the boiler broke a bit headachy at times???
maybe at last something is better in england than in scotland? my local council have to prioritise housing/repair problems where there are kids under 5 or adults over 70 in the house but I don't see why edinburgh city council would be any different?
phone again and lay it on, it may have been a case of them offering you a call out and if you didn't complain/let them know about your young child, they wouldn't ask anymore?