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.
The toxic trio has also been cited as a major source of the increasing pressure on local authority children's services.
However, the commissioner's analysis warned that the real toxic trio prevalence rate is likely to be higher than its estimate. This, it said, is because its estimate cannot factor in situations where the toxic trio issues are divided between the different adults within the household rather than concentrated in a single individual.
Click link below for related CYP Now content:
Special Report: Intrafamilial abuse special report
Analysis: Safeguarding pressures research reveals 'complex, urgent' issues
In tandem with the analysis, the commissioner has published a report highlighting the experiences of children living in toxic trio households.
"Much of the research into the impact on children of living in households with domestic abuse, parental substance misuse and mental health is from the perspective of adults - with limited insights from children themselves," said children's commissioner for England Anne Longfield in her introduction to the "Are they shouting because of me?" report.
The 15 children and young people interviewed for the report said they often felt frightened, depressed, angry and ashamed about the situation in their home. Some said their home lives had driven them towards self-harm, eating disorders and suicide. Others said they felt responsible for their parents' behaviour or regarded their family situation as normal because they grew up with it.
A common theme was a fear of talking to other adults or professionals about the problems at home. Some said their parents would warn them never to speak to anyone about what goes on at home and others reported being worried that they would get taken into care if they told anyone.
Some of the children said they found telling professionals about the problems a negative experience and that being taken into care was just as traumatic as life at home.
"My mum was so angry with me, I've never seen her so angry," recalled one 15-year old girl.
While some hated the problems their parents faced and the disruption, stress and fear it causes them, they remained loyal to their parents. "Because I have love for my mum I just forgive her, I would never hold a grudge against her," said one 14-year-old girl.
Children interviewed for the report said they found it easier to speak to professionals they had built up a relationship with over a period of time such as teachers about the issue.