In a joint statement, Welsh First Minister Carwyn Jones and Scottish First Minister Nicola Sturgeon complained that the bill did not guarantee that powers brought back to Britain from the European Union would be handed down to the regional governments, instead handing them to central government first, with a promise that where appropriate they will be devolved further.
Introducing the legislation today, the Secretary of State for Exiting the European Union, David Davis, said: "This Bill means that we will be able to exit the European Union with maximum certainty, continuity and control".
May's government began the two-year withdrawal process on March 29, setting Britain on an uncharted journey.
"My issue was that this is incredibly important for the Swedish government and for the European Union and that it has to be made much more detailed in order to assure European Union citizens that they can rely on their rights".
Liberal Democrat leader Tim Farron said his party would join Labour in giving May "hell" on the bill.More news: Russian-American lobbyist says he was in Trump Jr.'s meeting
In a separate interview, Blair said he thought it was possible that Britain could stay in the European Union because public opinion was moving against Brexit.
The Great Repeal Bill is set to be published by the Government, which has resulted in mass debate on social media.
She wrote: "Many children I have spoken to over the previous year have told me they are very anxious about the uncertainty surrounding their status after Britain leaves the EU".
In its environmental briefing document, the government stated: "We remain committed to safeguarding and protecting the UK's long history of environmental protection".
"Yet their proposal makes residence rights dependent on European Court of Justice jurisdiction, something which won't be agreed until the end of the negotiations".
"Rational consideration of the options would sensibly include the option of negotiating for Britain to stay within a Europe itself prepared to reform and meet us halfway", Blair, who was prime minister from 1997 to 2007, wrote.
In his piece he insists that such a compromise should be up for negotiation.