Story highlights Labour said it would try to keep Britain in the EU single market

It would immediately guarantee the rights of EU citizens in Britain

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."

Labour's Keir Starmer outlines his party's vision for Brexit in London on Tuesday.

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.

Read More