The drive, which will run across TV, press and radio is the first "health harm" anti-smoking campaign for five years and the first to roll out since the closure of the COI on Friday (30 March).
It follows a call at the end of last year by the British Medical Association to ban smoking in cars.
The TV execution, created by Dare, aims to communicate that 80% of "secondhand" smoke is invisible and contains harmful cancer causing toxins and poisons that are damaging children, even if the adult is smoking by a window or a backdoor. It shows smoke swirling around a sleeping baby.
Health Secretary Andrew Lansley said: "We all know smoking kills but not enough people realise the serious effect that secondhand smoke can have on the health of others, particularly children.
"This campaign will raise awareness of this danger and encourage people to take action to protect others from secondhand smoke," he added.
Lansley said the campaign was "just one part of our wider strategy on tobacco", citing the closure of tobacco displays in large shops which comes into force next week. "We will also be consulting on plain packaging this spring," he said
Department of Health marketing director Sheila Mitchell said: "This new national secondhand smoking campaign is one of the most iconic, hard-hitting campaigns we have launched in several years. There is a generation of young people that haven't been exposed to a large national smokefree campaign which focuses on health harms.
"So, the time was right to remind people of the serious impact secondhand smoke has on others, especially children," she added.