An initial proposal a year ago by Britain that devolved powers returning from the European Union after Brexit should initially pass to Westminster was roundly rejected by Welsh and Scottish politicians.
Scottish Brexit Minister Michael Russell said he hoped May's team would accept his proposed solution of amending the clause allowing the U.K.to change European Union laws affecting Scotland, and said the U.K government needed to show more flexibility in future talks. The Scottish Government has said it can't accept it without amendments.
Bruce Crawford, the head of the Parliament's Finance and Constitution Committee, said the vote was a "historic and significant" moment for Scotland and that he hoped the government in London would "respect the views" of the assembly.
Theresa May has the power to force the Bill through without getting the consent of Scotland.
Scottish ministers contend that the devolved parliaments should have to give express consent for changes to these frameworks, while the United Kingdom side argues that this would effectively give MSPs the power of veto over frameworks extending right across the country.
"This is not some abstract issue - this covers key policy areas such as farming, food and drink, fisheries and protecting the environment", Russell added.
Lawmakers in the devolved Edinburgh assembly voted by 93 to 30 to refuse "legislative consent" for the highly-contested European Union (Withdrawal) Bill now being debated by the British parliament.
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"There is a clear solution which is, as I have said and as the committee agreed last week, to simply remove [clause 15] from the bill".
But Mr Russell warned: "The UK Government can not ignore the reality of devolution or try to drown out what this Parliament says".
He will call on him come to Scotland and hear "hear the concerns of all parties and to discuss with the Scottish Government and the UK Government any new ideas from any of the parties".
"Those changes mean that, when we leave the European Union, power will be held closer to people and communities across the UK". "But I don't think they should underestimate it".
"These plans have been backed by the Labour Government in Wales". Nicola Sturgeon, Scotland's first minister and leader of the SNP, said Britain was headed towards "uncharted constitutional territory".
"Sadly we know that the Tories" understanding of the word "consent' is a farce, and that they are determined to put a wrecking ball through the devolution settlement regardless".
'There is still time to fix this mess'.