Prime Minister Theresa May must seek the consent of all nations of the UK, including Scotland, Wales and Northern Ireland, in a bid to secure a lasting Brexit deal, a cross-party group of peers said on Wednesday 19 July.
The House of Lords' EU Select Committee, chaired by former Conservative MP Tim Boswell, also warned May against using the UK's split from the EU as a "power grab".
"Brexit will be a major constitutional change for the United Kingdom, and thus potentially a source of instability," said Boswell.
"Any attempt to use Brexit to make a power grab, either to 're-reserve' powers previously devolved, or to claim more devolved powers, could compound such instability: this is not the time to embark on controversial amendments to the devolution settlements.
"We therefore believe that the existing statutory balance of competences between the UK Parliament and the devolved legislatures should as far as possible be unchanged."
He added: "No durable solution will be possible without the consent of all the nations of the UK. Common standards will be needed to maintain the integrity of the UK single market, but these cannot be imposed top-down by the UK government.
"They must be developed in partnership with the devolved governments, respecting national, regional and local diversity."
The government has promised to seek the consent of all devolved legislatures over the Repeal Bill, the draft legislation going through parliament which is designed to put all EU law onto the UK statute book, but the group of peers said "more is needed".
"We urge the government to raise its game in making the Joint Ministerial Committee (European Negotiations) more effective," Boswell said.
Welsh First Minister Carwyn Jones and First Minister of Scotland Nicola Sturgeon have both said that they cannot back the Repeal Bill without changes to the draft law.
"We have repeatedly tried to engage with the UK Government on these matters and have put forward constructive proposals about how we can deliver an outcome which will protect the interests of all the nations in the UK, safeguard our economies and respect devolution," the leaders said in a joint statement.
"Regrettably, the Bill does not do this. Instead, it is a naked power-grab, an attack on the founding principles of devolution and could destabilise our economies."
The Department for Exiting the EU had not responded to a request for comment at the time of publication.