Jeremy Paul Wright QC is an English Conservative Party politician and lawyer who was Attorney General for England and Wales and Advocate General for Northern Ireland from 2014 to 2018, and has served as Culture Secretary since July 2018.
Efforts will resume on Monday to persuade the EU to agree changes to the "backstop" plan to prevent The Return of customs checks on the Irish border.
Labour says the Tories cannot be united and has called for cross-party talks.
The UK remains on course to leave the EU on 29 March. But Mrs May has been unable to convince a majority of MPs to back the withdrawal terms she struck with the EU last year.
The Prime Minister told MPs in The Letter she will return to Brussels to meet European Commission President Jean-Claude Juncker This Week , and speak to the leaders of every EU member state over the coming days.
Her main goal is to win concessions over the backstop, which is widely disliked by members of her party.
Many fear it will mean the UK staying closely aligned to EU rules for the long term, without Britain being able to end the Agreement unilaterally.
But EU leaders have.
The comments it said were leaked from a WhatsApp group suggesting ex-Brexit minister Steve Baker told fellow Brexiteers that Mrs May's talks with Brussels were a "complete waste of time".
However, Culture Secretary Mr Wright has hinted that there might be "A Number of different ways" around the problem.
"I don't think it's The Mechanism that matters, it's The Objective ," he told the BBC's Andrew Marr Show, when asked whether a codicil - a supplementary document explaining or modifying a legal Agreement - might work.
"Parliament needs to give the Prime Minister space to have that conversation with Brussels," he added.
Attorney General Geoffrey Cox , who has if Brexit trade talks break down, will set out what changes would be needed to address concerns in a speech on Tuesday.
If MPs do not approve a formal deal, many fear chaos at ports and for business.
"We have put our proposals on the table; we're willing to negotiate around those," he said. "They're the basis of what we think could secure parliamentary approval, but she has to start negotiating as well. "
The PM's negotiating stance has never been "based upon mutual interest or mutual respect" but was "about banging the table and walking away", he added.
Asked about the prospect of a further referendum, Mr McDonnell said The Party 's priority remained a Brexit deal that protected jobs and the economy.
Campaigners for another referendum on Brexit have said there will be a major protest the weekend before Britain's scheduled departure date on 29 March.'Failure to make compromises'
In her letter, Mrs May described the latest Commons defeat over her Brexit strategy, in which dozens of Conservatives abstained on Thursday, as "disappointing".
"I do not underestimate how deeply or how sincerely colleagues hold the views which they do on this important issue - or that we are all motivated by a common desire to do what is best for Our Country , even if we disagree on the means of doing so," she writes.
"But I believe that a failure to make the compromises necessary to reach and take through Parliament a withdrawal Agreement which delivers on the result of the referendum will let down the people who sent us to represent them and risk The Bright future that they all deserve. "'No change in tactics'
Analysis by Peter Saull, BBC political reporter
The PM believes the only way to get a deal through The Commons and keep her party together is by securing changes to the backstop, even if the EU shows no sign of budging.