Cross-border divorce, child custody battles and business disputes could become longer and messier unless the UK can secure agreements to maintain judicial co-operation arrangements with the European Union after Brexit.
In a position paper published on Tuesday, the Government set out proposals to ensure that cross-border legal disputes are dealt with in a "fair and sensible way" post-Brexit.
The paper comes ahead of the third round of formal Brexit talks which begin in Brussels next week.
The Government said that "coherent commons rules" for how civil cases will be dealt with following withdrawal, will be "vital" for millions of families, businesses and consumers.
It goes on to state that close judicial co-operation will be "crucial" for millions of EU citizens living in the UK, and Britons living on the continent, as well as businesses which buy, sell and invest across borders, and the many ordinary people who get caught up in legal disputes.
The UK is seeking a new arrangement which would "mirror closely" the current EU system for deciding which country's courts will hear a case, which country's laws will be used to resolve it, and how judgements in one country will be enforced in another.
The proposals are designed to cover a wide-range of cases such as Britons involved in divorce, custody and child maintenance battles with EU-born spouses, companies suing continental suppliers, or consumers seeking compensation for faulty European goods.
If no deal is reached, UK citizens could find themselves forced to fall back on international rules set out in agreements such as the Hague Convention, which officials acknowledge are slower and less effective than the EU system.
It could also mean that court cases are launched in the UK and in an EU country without agreement on which ruling is definitive.
Currently the UK is part of the EU's civil judicial co-operation system which provides a clear set of rules to manage cross-border disputes.
The proposals are the latest in a string of papers which set out the Government's position ahead of the third round of Brexit talks which begin in Brussels next week.
The most contentious paper is expected to be one on the future relations with the European Court of Justice (ECJ), which is expected in the next few days.
Tuesday's paper calls for a new reciprocal framework for civil law based on commitments to build on existing co-operation and to continue collaboration across borders.
So far, the European Commission has so far set out proposals only for dealing with cases already under way at the time of Brexit.
David Davis is now pressing for early discussion on the arrangements for co-operation after the UK leaves the direct jurisdiction of the ECJ.
Announcing plans to seek "new close and comprehensive arrangements" for civil judicial co-operation with the EU, reflecting "closely" the existing rules, the UK Government paper states: "We have a shared interest with the EU in ensuring these new arrangements are thorough and effective.
"In particular, citizens and businesses need to have continuing confidence as they interact across borders about which country's courts would deal with any dispute, which laws would apply and to know that judgments and orders obtained will be recognised and enforced in neighbouring countries as is the case now."
The paper states that the current EU arrangements deliver "predictability and certainty" and play "an important role" in enabling businesses to trade with confidence across borders, providing legal certainty in cross-border transactions and avoiding delays and excessive costs in family cases.
"The best way to ensure legal certainty for both UK and EU citizens and businesses as we leave the EU is to facilitate a smooth transition to a new relationship in civil judicial co-operation," it says.
The paper also calls for an interim period to allow citizens and businesses on both sides to plan ahead, allowing "for a smooth and orderly move from our current partnership to our future partnership".
It also makes clear that the UK intends to apply for membership as an individual country of international judicial agreements in which it currently participates through its EU membership, including the Hague Conventions and the Lugano Convention.
Last week the Government released a position paper in which it said it was "confident" it could enforce new immigration controls on EU citizens without needing to enforce a hard border between Northern Ireland and the Republic of Ireland.
Avoiding checkpoints is one of the top priorities for negotiating post-Brexit arrangements for its only land frontier with the EU.
As well as the position paper on future relationships with the ECJ, the Government is also expected to publish three more position papers in the coming days.
One document on goods will emphasise that the Government is seeking a deal to ensure the freest and most friction-less trade possible in goods and services.
Another will focus on confidentiality and make clear the Government's intentions on ensuring official documents and information exchanged between the UK, EU and other member states remain protected after Brexit.
While a final paper on data will seek to ensure that it continues to be passed between the UK and EU without disruption.