Ms Sturgeon and Labour’s Carwyn Jones, her Welsh counterpart, wrote to Mrs May demanding 38 amendments to the EU Withdrawal Bill in return for recommending their parliaments give the thumbs up to the new law.
They want all 111 EU laws and regulations which involve devolved powers – originally created by the UK Government – to be handed directly to parliaments in Cardiff and Edinburgh.
But the Prime Minister’s deputy Damian Green hit out at the Scottish First Minister, saying they would end up “doing things four different ways” in the UK’s four nations – increasing costs for consumers, companies and workers.
Although some powers from Brussels would be devolved the Government would “do nothing that risks undermining the benefits” the the UK’s own market, he warned.
The Government gave a number of examples from Ms Sturgeon’s lengthy list of EU rules she wants to keep for Scotland, including food labelling, pesticides and infectious disease control in animals.
Mr Green said: “The important thing now is to work our way through these lists and find the areas where we will need to maintain a common UK or GB approach, as well as those areas where it will make sense to transfer powers direct to the devolved governments.”
He added the UK Government would “not risk our internal UK market, or make life more difficult or more expensive for UK companies, workers or consumers”.
Jackson Carlaw, the Scottish Tories’ deputy leader, said: “Unfortunately, the SNP’s record on Brexit over the last year has been to sow division and use it to push for a second referendum. We genuinely hope there is now an opportunity for a fresh start.”
Ms Sturgeon and Mr Jones claimed they should be allowed the same “Henry VIII” powers as UK ministers so Scottish and Welsh laws can be changed without parliament’s full approval.
In the letter, they also demanded UK ministers needed to get consent on “necessary changes” to EU law in devolved areas after Brexit.
The pair said they were “ready to work in a cooperative and coordinated way with others to prepare for Brexit” but said the Bill was hampering cooperation.
They said the Bill must be “substantially amended” before their parliaments could consent and claimed their 38 amendments were a “constructive contribution” to protect the “hard-won devolution settlements of the UK”.