The Welsh and Scottish First Ministers have urged peers to block what they have called a Brexit "power grab" by the UK government.
The UK government wants to keep control of 24 EU policy areas temporarily to preserve trade within the UK.
Carwyn Jones and Nicola Sturgeon have now written to the House of Lords calling for changes to the EU (Withdrawal) Bill.
They claim powers held back include areas of "vital importance" to them.
The EU (Withdrawal) Bill - currently being examined in detail at committee stage in the Lords - aims to ensure the rules currently set by European law still apply in the UK after Brexit, while giving the UK Parliament power to change them.
As the bill currently stands, powers in devolved areas that are currently wielded at EU level - such as support for farmers - are set to return to Westminster rather than Cardiff, Edinburgh and Belfast.
Last week UK ministers announced the list of powers that they would retain at a UK level, for a temporary period, including food labelling and chemicals regulation.
Cabinet Office Minister David Lidington said at the time that the "vast majority" of Brussels powers in 158 devolved policy areas would be in the control of Wales and Scotland "on the day we leave the EU".
But he added: "There is a much smaller group of powers where the devolved governments will be required to follow current EU laws for a little bit longer while we work out a new UK approach."
In the letter to peers, Mr Jones and Ms Sturgeon said these covered areas of "vital importance" for the industries and economies of Wales and Scotland.
They said they agreed "common frameworks" for UK-wide policies were "appropriate in some cases" but rejected the idea of letting UK ministers set them up without approval from Cardiff Bay and Holyrood.
"The devolved legislatures would be asked to agree to the creation of this power with no certainty about where frameworks will be established, how these will work, how they will be governed and how we will go from temporary restrictions to longer term solutions," the first ministers said.
The letter asks for changes to the bill to ensure that any such frameworks or restrictions on devolved powers could not be introduced without consent from the Welsh Assembly or Scottish Parliament.