By Angela Dewan CNN

LONDON (CNN) -- Britain's main opposition party has vowed to scrap Prime Minister Theresa May's Brexit plans if it wins the general election in June, saying it will seek a softer departure from the European Union.

Labour's Brexit spokesman Keir Starmer said that, if elected, his party would guarantee EU nationals living Britain the right to remain in the UK after the split, and would be open to retaining the benefits of the EU's single market and customs union.

Laying out his party's vision for Brexit in London on Tuesday, Starmer sought to offer British voters a clear alternative to May's plans for a \"hard Bexit.\"

May has said that she favors a clean break -- leaving the single market and removing the UK from the obligation to allow unlimited migration from the EU, known as \"freedom of movement.\"

But Starmer said that May's Brexit vision was \"reckless\" and that the June 8 election was fundamentally a vote on what kind of Brexit the British people wanted.

\"We do not accept that Brexit has to mean whatever Theresa May says it means. We do not accept that there has to be a reckless Tory Brexit,\" he said, using the colloquial name for May's Conservative Party.

\"We have a very different vision, a vision now about how Brexit can work for Britain and the EU.\"

Starmer said that a Labour government would rewrite May's Brexit negotiating strategy and would focus instead on a deal that retained as many of the benefits as possible of the single market and customs union.

He said a Labour government unilaterally guarantee the rights of EU citizens living in Britain \"on day one,\" and would seek to ensure the rights of British nationals living in the EU.

May called an early election less than halfway through her government's five-year term.

She said she was seeking a clear mandate from the people for her Brexit plans and to quell opposition in Parliament to her plans. May's party only has a slim majority in Parliament, but opinion polls suggest that her party will win a greater number of seats in June.

May also faces divisions in her own party over Brexit tactics.

The UK government formally served divorce papers on the European Union on March 29, signaling the beginning of the end of a relationship that endured for 44 years.

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