Smoking in cars that are carrying children has already been banned in some states of Canada, Australia and the US and the whole of South Africa.
Canada's Cancer Advisory Coalition claims the states' bans on smoking in cars have reduced children's exposure to second-hand smoke by 33%.
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Two-year-old Casper Platt-May and his six-year-old brother Corey died in the crash in Coventry on Thursday.
It means the petition, calling for a diverse panel to be appointed to the inquiry, has enough signatures to spark a debate in Parliament.
American businesses have begun severing ties with controversial pro-gun group the NRA in the wake of the latest mass school shooting.