This means the deal could be voted through the House of Commons, but a second referendum could be held before that deal takes effect.
May has said she has compromised on ten key points, but Al Jazeera's Laurence Lee says most of the "concessions" were already known, and the only new offer was that of the confirmatory referendum. "But I recognize the genuine and honest strength of feeling across the House on this important issue".
Ministers will begin discussions on Monday on a package of measures to be included in the forthcoming Withdrawal Agreement Bill (WAB) aimed at securing cross-party support.
The British government's Brexit Withdrawal Agreement Bill needs to include another public vote when it is presented to lawmakers again next month, the opposition Labour Party's Brexit spokesman Keir Starmer said on Saturday.
A strong polling performance for The Brexit Party put Sterling on its back foot last week but losses accelerated after opposition leader Jeremy Corbyn withdrew from cross-party talks aimed at agreeing a future relationship with the European Union that could secure a parliamentary majority, sending the Pound-Euro rate -1.48% lower by Friday.
"This will be reviewed if he is willing to support Conservative candidates at future elections". They want to replace her with a staunch Brexit supporter such as Boris Johnson, a former foreign secretary.
He said: "It's changed from being the start of a process a new leader could potentially run with, to being a weight round the neck of a new leader".
The current deadline to leave is 31 October.
May held six weeks of talks with the main opposition Labour party on a possible compromise to help push the Brexit deal through parliament, but the two sides announced on Friday that the talks had ended.
The "new deal" is an attempt by the prime minister to win over critics across the House of Commons who have rejected her three previous attempts to get an agreement through.
However, Jeremy Corbyn said he had heard nothing yet from the Government that would persuade him that Labour should now fall in behind her Withdrawal Agreement with Brussels.
The DUP, on whose support May depends to command a majority in parliament, says efforts to avoid a "hard border" between Northern Ireland and the Republic of Ireland - keeping Northern Ireland largely aligned with the European Union until a new trade deal can be agreed, also known as the "backstop" position - undermines the integrity of the United Kingdom, creating a trade border between Northern Ireland and Great Britain.
Customs is a major bone of contention between the parties.
In a sign of the splits within the Conservative government over Britain's departure from the EU, Treasury chief Phillip Hammond cautioned against trying to leave the bloc without an agreement on trade and other terms.
Despite the collapse of cross-party talks with Labour, the Bill contains a series of commitments on workers' rights and environmental protections created to appeal to Opposition MPs.
"This deal lays the groundwork and settles numerous core issues, but in the years ahead Parliament will be able to debate, decide and refine the exact nature of our relationship with the EU".
"It is practical. It is responsible".
Mr Snow said: "Sounds like we're going to give him a thorough spanking" to which he replied: "I'm going to have a full and frank exchange of views but without coffee in his case".