Fathers will get improved contact with their children following divorce, amid plans to rewrite the law governing custody disputes.

A ministerial working group will decide how to amend the Children’s Act 1989 and might include in it a “presumption of shared parenting”. The changes are part of an overhaul in family law that is described by the Law Society as “the most important” in more than 20 years.

Currently, family courts decide to leave children with their mothers in the vast majority of divorce cases, meaning that one in three children – around 3.8 million – is living with their father absent from their lives. Just 8% of single parents in Britain are fathers living with their children, according to the Office for National Statistics.

The plan, to be published on Monday, will overturn the main finding of an independent official review into family justice conducted by economist David Norgrove, which reported in November. He concluded that it would be too onerous for judges to ensure greater equality of access.

The working group, comprising education ministers Tim Loughton and Sarah Teather, and justice minister Jonathan Djanogly, has been asked to come up with proposals on how the law should be changed within two months.

Loughton said: “Where cases do end up in court, we believe it is important that children don’t lose contact with their parents, unless there are concerns about safety or welfare.

“But there is a familiar picture in the UK of parental separation leading to thousands of children losing meaningful contact with the ‘non-resident parent’ – usually the father.

“It is right that we consider all the options to help ensure that children can continue to have an ongoing relationship with both their parents after separation.

“This issue affects the lives of hundreds of thousands of children, and it would be negligent not to. It is also right that we continue to encourage fathers to take responsibility as equal parents and to be fully involved with their children from the outset.

“The state cannot create happy families, or broker amicable break-ups. But if children are having decent, loving parents pushed out of their lives, we owe it to them to change the system that lets this happen.”

Fathers4Justice, the campaign group, has claimed that each day 200 children lose contact with their fathers because of rulings in the family courts. But ministers are bracing themselves for a backlash from single mothers’ groups whose members are concerned about the possibility of aggressive fathers intervening in the lives of their children.

The government is also providing a further £10m for mediation services to encourage more couples to settle their disputes out of court. Ministers believe that mediation offers a less confrontational and generally faster method of resolving arguments about assets and care of children after the breakdown of a relationship than the family courts.

Loughton added: “The courts are rarely the best place for resolving private disputes about the care of children.”