Conservative MP Oliver Letwin arrives for a cabinet meeting at number 10 Downing Street, in central London, Britain July 12, 2016. REUTERS/Neil Hall

LONDON (Reuters) - The British parliament should be given the opportunity to find an alternative way to leave the European Union and lawmakers would support a Norway-style post-Brexit relationship, Conservative lawmaker Oliver Letwin said on Thursday.

“The idea is: if the prime minister doesn’t get her deal across the line next week... we need to try to establish whether there is a cross-party majority for some alternative,” said Letwin, a former cabinet minister in David Cameron’s government,

“The idea would be to have a day where members of parliament across the parties can bring forward alternative propositions and see whether, as I hope, and believe, it will be possible we can get a majority for some alternative.”

Letwin said he felt parliament would support a Norway-style relationship with the EU.

“I believe that we will probably on that day be able to get a cross-party majority in favor of what is sometimes called Norway-way plus,” which would involve staying in the EU’s single market and a customs union, Letwin said.

He warned that if May’s deal fails again and parliament was not given indicative votes, then the United Kingdom faced a potential no-deal exit.

“Then we are headed for a no-deal exit,” he said.