Families and businesses could face "real hardship" after Brexit unless cross-border agreements on civil justice are replaced, a Lords committee has warned.
Peers said Brussels regulations play a "significant role" in the lives of UK and EU citizens, providing "certainty, predictability and clarity" over legal disputes in areas such as divorce, child custody and employment.
The House of Lords EU Justice Sub-Committee highlighted the current system of "mutual recognition" of judgments across the EU.
If the regime is not duplicated, families and businesses could be subject to national rules across the 27 other member states, the peers said.
A report from the committee sets out hypothetical examples where EU regulations could be used, such as to determine where a cross-border dispute between a manufacturer and supplier should be heard.
Ministers have pledged to bring an end to the jurisdiction of the Court of Justice of the EU (CJEU) in Britain as part of the Brexit settlement.
The committee's report said: "If the Government continues to apply its anti-CJEU stance too rigidly it will severely limit its post-Brexit options for adequate alternative arrangements.
"It is clear that regardless of the outcome of the Brexit negotiations, civil justice co-operation of the type dealt with by these regulations will remain a necessity.
"We are in no doubt that without adequate alternative arrangements post-Brexit there will be great uncertainty for UK businesses and citizens."
The peers said the Government "has not taken account of the full implications of the impact of Brexit" on the areas of EU law covered by three civil justice regulations dealt with in the report.
"In the area of family law, we are very concerned that leaving the EU without an alternative system in place will have a profound and damaging impact on the UK's family justice system and those individuals seeking redress within it," the paper concluded.
Committee chairwoman Baroness Kennedy of The Shaws said the panel heard "conclusive" evidence that there is no means by which reciprocal rules can be replicated in a Great Repeal Bill.
She said: "Domestic legislation can't bind the other 27 member states.
"We therefore call on the Government to secure adequate alternative arrangements, whether as part of a withdrawal agreement or a transitional deal."
A Government spokeswoman said: "The UK has led the way in terms of civil judicial co-operation, and this will not change after the UK leaves the EU.
"We are confident that our allies in the EU will work with us to ensure a seamless transition.
"It is clearly in our mutual interest to maintain a framework that serves and protects families, consumers and businesses.
"In terms of family law, we recognise the crucial importance of certainty and clarity and avoidance of delay for children and families involved in disputes."