Of 3,000 parents or carers of young people aged between 10 and 17 surveyed by The Children's Society, 12 per cent reported that health professionals or family members were concerned about their drinking or had advised them to cut down over the last five years.
This equates to the parents or carers of 700,000 children if applied to the UK population, according to the charity. Of these, the same parent also suffered from depression or anxiety in 59 per cent of cases and 39 per cent of young people had experienced domestic violence.
In addition, 29 per cent of young people living in a home blighted by alcohol abuse had been homeless in the last five years.
The survey's findings also suggest that 1.6 million young people have a parent with depression or anxiety and 1.7 million are living in homes struggling with debt.
The Children's Society has warned that the pressure of living in a home where alcohol or drugs are being abused can lead to them developing mental health problems, running away from home or being excluded from school.
One teenage girl whose father was abusing alcohol told the charity: "After living with my dad for about six months, I started really, really lashing out. I was getting really angry. And all the built up anger had just sort of exploded. And I started doing horrible things… I turned into somebody else for a while. I can't say I blamed my dad for it, but he's the reason behind it."
The survey also found that a quarter of young people in homes affected by alcohol abuse were taking on caring responsibilities, including taking care of siblings or nursing parents.
"Millions of teenagers in the UK are suffering in silence with problems that would floor an adult," Matthew Reed, chief executive of The Children's Society said.
"The hundreds of thousands of children whose parent has a drinking problem are sadly just the tip of the iceberg of children in desperate need of support."
Reed said he is also concerned that specialist support for families affected by alcohol abuse is being eroded by public sector funding cuts.
"At a time when demand for council children's services is rising, severe funding cuts from central government are leaving more and more to deal with these huge problems alone," Reed added.
"Without support at an early stage as problems emerge, these families can quickly reach crisis point and the risks for the children involved grow."
The Local Government Association said councils are facing a £2bn funding gap in providing children's services by 2020, which is limiting spending on early intervention support, including specialist help for families affected by alcohol and drug abuse.
"We know that both children and adults' mental health services are under growing pressure, while public health funding, which pays for vital alcohol treatment programmes and other community support, has been cut by more than half a billion pounds by the government in the last five years," Richard Watts, chair of the LGA's children and young people board, said.
"Councils aim to help struggling families at an early stage, before issues become serious, but demand for child protection support has increased dramatically at the same time as local authority budgets from central government have faced significant cuts.
"This is forcing many areas to make extremely difficult decisions about how to allocate increasingly scarce resources, and early help services have seen their funding reduced as councils are forced to prioritise urgent help for children at immediate risk of harm."
- The November edition of CYP Now magazine includes a special report on intrafamilial abuse