London: British Prime Minister Theresa May on Tuesday set out what she called a "new" Brexit deal, with safeguards and legal assurances on aspects of her controversial withdrawal agreement in the hope of getting cross-party backing for the bill when it returns to the House of Commons next month.

In a major compromise to a demand from the Opposition benches, she promised to include the option of a parliamentary vote on holding a second referendum on her deal if it clears the Commons next month.

"I recognise the genuine and sincere strength of feeling across the House on this important issue. The government will therefore include in the Withdrawal Agreement Bill at introduction a requirement to vote on whether to hold a second referendum, she said in a speech in London on Tuesday.

"This must take place before the Withdrawal Agreement can be ratified, she noted, even as she reiterated her continued opposition to holding another referendum.

If the House of Commons were to vote for a referendum, it would be requiring the government to make provisions for such a referendum. So to those MPs who want a second referendum to confirm the deal: you need a deal and therefore a Withdrawal Agreement Bill to make it happen, she added.

In what she termed as a last chance to deliver the result of the June 2016 referendum in favour of Brexit, the British PM made some further commitments on a temporary customs arrangements and caveats on the Irish backstop in an attempt to win over more MPs to vote in favour of her Brexit agreement, defeated three times by Parliament by falling margins.

Should the backstop come into force, the government will ensure that Great Britain will stay aligned with Northern Ireland. We will prohibit the proposal that a future government could split Northern Ireland off from the UK's customs territory, she said.

Her speech also covered a set of additional votes for the Parliament to decide on whether to impose a temporary customs union with the EU until a more permanent solution is found, in an attempt to placate the Opposition Labour Party.

Assurances on workers' rights and the environment were among some of her additional commitments to see the withdrawal bill through Parliament.

The Withdrawal Agreement Bill, a legislation required to bring the withdrawal agreement negotiated with the EU into British law, is set to come up for a fourth Commons vote in the week beginning June 3. May has already announced plans to set a timetable for her exit as British PM once the bill returns for its next major parliamentary clash next month