No matter how austere, the child rearing environment was more conducive than when bombs were falling, men were fighting overseas and women were engaged in war work.
People were happy that the war was over (and had beaten the enemy!); men returned to the factories, women returned to the home. "The family" became a viable option once again and so more people had children than during the war years. Why would you think that all this would have no effect on the birth rate?
Baby Boom = More births than previous birth trend.
Are you suggesting that in those previous years (e.g. 1939-45) there were fewer smokers? Is it not reasonable to assume rates of smoking (approx 80% ???) were very similar immediately pre-war and post-war? If so, there is no reason to bring smoking into the Baby Boom equation - you are comparing like for like in regard of smoking and so it is irrelevant. Smoking may only become a relevant factor when comparing years where smoking rates are appreciably different but then you have to also allow for other lifestyle changes.
Birth rates are currently lower than 1946-1960; a time before the contraceptive pill, abortion was illegal, few women had careers - and smoking was more prevalent. Realistically, which of these changes is likely to have had the least effect on birth rates?