The money, being provided through the Innovation Fund for Children of Dependent Drinkers, which is managed by Public Health England (PHE), will be used to run projects with a "new and creative approach" to supporting families affected by alcohol.
It is hoped that the projects will help identify more children and parents affected by alcohol, increase the number of parents receiving treatment for their addiction and reduce parental conflict.
Among local authorities to receive funding is Swindon Borough Council, which will use the money to run a parenting programme for 840 parents and help 370 children with alcoholic parents.
And Knowsley Council will train 1,000 professionals to identify potential alcohol dependent parents. The project aims to see a 20 per cent increase in the number of alcohol dependent parents receiving treatment over a 12-month period.
Identifiction is also at the heart of North Tyneside Council's successful funding bid. It is hoping to double the number of children who are identified as living with alcoholic parents and increase the number of parents receiving treatment by 50 per cent.
Supporting alcohol dependent parents leaving prison, as well as their children, is the focus of a joint project across five Greater Manchester local authorities: Rochdale, Bolton, Bury, Salford and Trafford.
Elsewhere, Brighton and Hove Council's successful bid will see the council focus on adult and children's services working together to better identify vulnerable and neglected children and their alcoholic parents.
Other councils to receive funding to support families affected by alcohol dependency are St Helens, Portsmouth and Haringey.
An additional £6m capital fund for councils has also been created to improve facilities and services for people with alcohol problems between 2019 and 2020. Councils have until 21 January to submit bids for this fund, with successful projects announced next spring.
It is estimated that there are 200,000 children in England living with 120,000 parents with alcohol problems.
PHE data for 2017/18 shows there are 16,000 adults receiving treatment in relation to alcohol while living with children. There are a further 18,000 parents being treated who are not currently living with their children. Most children (82 per cent) with parents receiving help with alcohol problems are not receiving support from children's social care, adds the figures.
PHE adds that parental conflict where alcohol is a factor can harm children in later life, affecting their education and employment opportunities.
"Alcohol abuse can tear lives apart, not only for the people trapped in the grip of an addiction but for their children, who are often robbed of the support, comfort and structure they need from their parents," said public health minister Steve Brine.
"I am committed to finding new ways to help families in the midst of these heart-breaking situations. Many children in this position suffer in silence - but the funds awarded to these councils today will help them identify those children sooner and offer them a vital lifeline."
Local Government Association community wellbeing board chair Ian Hudspeth added: "The causes and the solutions for tackling alcohol misuse are multi-factorial. It requires close working with partners, imagination and hard work.
"However, when we get it right it can have a tremendous impact on the lives affected."
Meanwhile, the PHE has updated guidance for councils on safeguarding children with alcohol and drug dependent parents.
This emphasises the need for a "whole family approach" to supporting parents with alcohol problems and their children, involving adult alcohol and drug treatment services and children and adult social care working together.