He says it is conceivable that there is "no majority in parliament for any Brexit deal" and that in those circumstances they had to look at all options.
"And so you keep your options open".
He said: "We've now got two propositions, we've got the Labour proposition which I think has the majority support in Parliament, and the Prime Minister's new proposition, let's put it to a vote".
May categorically said she won't commit to a second vote "because the British people voted, made their choices and want their government to deliver..."
Adding: "Is the current meltdown in the Government good for anyone?"
UK's foreign secretary, Boris Johnson, resigned Monday following the resignation of Brexit's top leader, David Davies, hours earlier, in a sign the United Kingdom government is crumbling while trying to negotiate a deal to leave the European Union. "It's time for the Labour party to give up the idea of a second referendum".
The leader of Britain's opposition Labour Party, Jeremy Corbyn, accused Prime Minister Theresa May of being incapable of negotiating a Brexit deal with the European Union given the deep splits among her own ministers over her plans.
"And so you keep your options open", he said.
The shadow Brexit secretary said Labour was not explicitly calling for a public vote on the final deal and respected the result of the 2016 referendum.
He suggested that the best interests of the United Kingdom and the best economic interests of the United Kingdom "are not the same thing" - and the referendum result had to be respected.
He told BBC One's Andrew Marr Show: "I'm afraid it's got fudge written all over it".
Theresa May's Brexit plans are "unworkable" and a "fudge", the shadow Brexit secretary has claimed.
Lord Adonis said: "What I think should happen when we see her deal, given that it's going to be a betrayal of our economic national interest, jobs, people's livelihoods, people's incomes are going to be at stake, the right thing for us to do then is to have a people's vote".
- Champions League is target for record City signing Mahrez
- Space launch towers demolished at Cape Canaveral
- Chelsea winger Kenedy joins Newcastle on season-long loan
- Vettel wins British GP in thrilling finish - British Grand Prix 2018
- TicWatch Pro available now: why you’ll want one
- Woolworths recalls savoury rice after listeria outbreak in Europe
- Ahead Of Nawaz Sharif's Arrival In Pakistan Today, Gag Order On Media
- Fatal Flash Floods Hit Hiroshima, Japan
- What would a new Air Force One look like under Trump?
- MLB All-Star Futures Game 2018: Date, start time, rosters, how to watch