The Conservatives said only they had a clear plan for exiting the EU.
Ahead of a campaign visit to Wales on Tuesday, Theresa May said the Brexit vote should have been a "wake-up call for a generation of politicians who have taken the people for granted for too long", but instead other parties had "closed ranks".
The Conservatives are hoping to take seats from Labour on 8 June in areas which voted to leave the EU, including the Midlands, the north-east and north-west of England and across Wales.
Most Labour MPs backed Remain vote in last year's referendum.
'No rolling back'
Labour has been criticised by, among others, former prime minister Tony Blair, for a perceived lack of clarity in its approach to Brexit.
Unlike the Lib Dems, it has ruled out offering a second referendum on the terms of any Brexit deal, but suggested Parliament could stop a so-called "hard Brexit".
In Labour's first major policy statement of the election campaign, the party is signalling it would take a different approach to the two-year process of negotiating the EU's exit - expected to start in earnest in June.
It says it would:
- Scrap Mrs May's Brexit plan - outlined in a White Paper in February - which envisages leaving the single market and customs union
- Focus on a deal that "retains the benefits" of both organisations
- Guarantee the legal status of the three million EU nationals living in the UK on its first day in office
- Press for a reciprocal guarantee for the 1.2 million Britons living on the continent
- Replace the government's proposed Great Repeal Bill - which would scrap the 1972 European Communities Act and transpose myriad existing EU laws applying to the UK into domestic law - with an EU Rights and Protections Bill
Labour also insists there can be no "rolling back" of workplace protections, environmental standards and consumer rights, and no measures to limit the lifespan of any EU-derived laws or directives, such as sunset clauses.
Speaking on BBC Radio 4's Today programme, Sir Keir criticised the prime minister's "rigid" approach, and said offering an immediate, unilateral guarantee to EU nationals living in the UK would be "received as a very welcome message" by Brussels negotiators and help "reset the tone" of talks.
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