The charity says 198,000 babies are born into homes where one or both parents are suffering from abuse, addictions and mental anguish.
It says that 144,000 babies under a year old are living with a parent with mental health issues. The charity calculates 93,000 babies have a parent with alcohol problems, and 50,000 babies have a mum or dad who has used illegal drugs in the past year.
The NSPCC report, All Babies Count, says the risk of homicide is greatest in a child's first three months and the perpetrators are "almost always parents".
Today the charity launches an early intervention campaign to reach parents of 80,000 newborns over two years in 12 hospitals, using a programme which cut hospital admissions in the US by 40 per cent. The charity is also setting up a trial using an Australian method of teaching early parenting that cuts the risk of child harm in families where the parents have drug addiction problems.
The report says that these vulnerable children are at more risk of greater issues surrounding their future learning, behaviour and health.
A study in New Zealand found youngsters with at least one problem-drinking parent was more likely to have "mood disorders, depression, anxiety, substance misuse and behaviour problems" by the age of 15.