Shadow Brexit secretary Keir Starmer said Labour would work with devolved nations to get the right Brexit deal and would ensure that all EU powers in areas that Holyrood currently has responsibility for would be handed to Scotland.
The SNP has accused the government of putting devolution at risk by suggesting it would hold on to powers in order to create UK-wide regulations for industries like agriculture and fishing and prevent against any internal trade barriers appearing after Brexit.
Setting out his party’s plan for tackling Brexit if Labour pull off a shock victory at the general election in June, Mr Starmer said he would scrap Theresa May’s Great Repeal Bill and instead legislate to protect all EU workplace and environmental protections in UK law.
He promised to give a unilateral guarantee to all EU citizens living in the UK “on day one”, saying it would “unblock” negotiations to secure a similar declaration for British nationals in Europe.
But he admitted that the EU referendum result meant the free movement of people had to end, and that the UK would therefore have to leave the single market.
Mr Starmer said the UK should be willing to forego striking its own trade deals with other countries in order to secure the best possible trading access with the EU. And he said Labour would keep UK regulations as close to European rules as possible to ease future trade.
On immigration, he said new limits and rules would have to be introduced, and suggested individual “communities” could be asked for their views about how many immigrants should be allowed into the UK.
Mr Starmer’s stance on immigration goes further than his leader Jeremy Corbyn, who said in January that he was not “wedded” to free movement of people but did not want to rule it out.
And there were signs that his strategy launch was being snubbed by the Labour leadership when a list of election priorities sent to Labour MPs was leaked, revealing that Brexit did not appear anywhere in the top “lines to take”.
In a speech in London, Mr Starmer said a Labour government would have a “presumption that any new powers that are transferred back from Brussels should go straight to the relevant devolved body.”
He said: “This will apply to regional government across England, as well as to the devolved administrations in Scotland, Wales and Northern Ireland.
“This was a proposal included by the Mayor of London in his Brexit White Paper and it is one a Labour Government will take forward.
“A Labour approach to Brexit will be part of a radical extension of devolution, and will help bring the country together.
“A Tory Brexit will push the country further apart and lead to a concentration of power in Whitehall.”
Speaking to the BBC on Tuesday night, Lord Mandelson said Labour is not “differentiating their position and their policy sufficiently from the government” on Brexit and has had an “equivocal and fence-sitting approach” so far.