The Office of the Children's Commissioner for England used data from a 2014 mental health survey of adults to calculate the figure, which it said is the best estimate yet of the toxic trio's prevalence.
The commissioner's analysis concluded that 420,000 children and young people under 18 are in homes where all three toxic trio issues are present to a "moderate" or "severe" extent.
It also estimated that 103,000 children and young people live in homes with "severe" parental mental ill-health, domestic abuse and parental drug and alcohol abuse.
Evidence shows the toxic trio has damaging consequences for children's wellbeing and outcomes, and has repeatedly emerged as a feature of cases subject to serious case reviews.
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