As the world awaits U.K. Prime Minister Theresa May's next move after her Brexit deal failed to obtain parliamentary approval, some politicians from the country's biggest opposition party believe a second referendum is now increasingly likely.

"The critical issue is now that she's been defeated in the House of Commons, what does Theresa May do and I think, there's only one way she can really go now — and that's towards a referendum to give the people a chance to sort out this crisis," Andrew Adonis, a Labour member of the upper house who previously served as U.K. transport minister and education minister, told CNBC on Wednesday.

Labour officially wants to push Brexit through even though swathes of the party consider themselves to be pro-EU. It tabled a no confidence vote against May, who is the head of the ruling Conservative Party, on Tuesday after her proposed Withdrawal Agreement lost by 230 votes. The deal details how Britain should exit the European bloc by end-March.

Labour leader Jeremy Corbyn is hoping May will lose the leadership vote, which will pave the way for a general election that Labour is likely to win. But many political analysts and some Labour politicians believe May will survive the no-confidence motion, unless Conservative lawmakers vote against their own party leader.