Mr. Mann, one of a small group of Labour MPs who have rebelled against Jeremy Corbyn and voted with the government on Brexit, has tabled an amendment which would give extra protections to workers and the environment.
Sterling hit a seven-week high against the dollar on Monday, 14 January, as Mrs. May delivered an upbeat speech on the eve of the Brexit vote.
The pound reached $1.2879, a level last seen in late November, after PM Theresa May issued a last-ditch plea for MPs to support her deal with the EU in the vote on Tuesday, 15 January.
The euro dropped to 0.88 to the pound, the lowest level since early December.
President of the European Commission Jean Claude Juncker issued a letter to Mrs. May on Monday in which he set out a number of reassurances on the Northern Ireland backstop and Mrs. May herself said, in her speech in Stoke-on-Trent, that the EU letters of reassurance on Brexit would carry legal weight in any future dispute.
Politics:— James Andrew (@jamesandrew48) 10 January 2019
John Mann's sentiment in putting down the amendment to protect workers rights in the Brexit future trade agreement is nice and all, but the amendment, as far as I see it, isn't legally binding. Can I trust Tories to enforce and protect workers rights? No, not overly.
"The letters published today have legal force and must be used to interpret the meaning of the withdrawal agreement, including in any future arbitration. They make absolutely clear that the backstop is not a threat or a trap. Now I fully understand that the new legal and political assurances which are contained in the letters of Donald Tusk and Jean-Claude Juncker do not go as far as some members of the parliament would like, but I am convinced that the members of parliament now have the clearest assurances that it is the best deal possible," Mrs. May said.
Theresa May's government has said it will "consider very seriously" supporting Mr. Mann's amendment in Tuesday's historic vote in Parliament.
“Whoever’s in government…has to give what I call the ‘real Brexit dividend’ into areas like mine”— Channel 4 News (@Channel4News) 10 January 2019
Pro-Leave Labour MP John Mann says “left behind” areas need their “fair share” after Brexit. pic.twitter.com/gSDKgzxrw6
Mr. Corbyn said Labour did not "accept or endorse" Mr. Mann's proposed amendment and he said the deal Mrs. May brought back from Brussels had been "quite clearly and emphatically rejected" by UK trade unions.
Mr. Mann represents Bassetlaw, a former coal mining area in Nottinghamshire, which voted resoundingly in favour of Brexit in the June 2016 referendum.
Labour had a majority of 17,000 in 1997 but that dwindled to less than 5,000 in 2017 and many traditional Labour voters who switched to UKIP in 2015 went for the Tories in 2017, rather than coming back to Labour.
While many Labour voters in the big cities and in university towns are strongly Remain, those in places like Bassetlaw, Sunderland and in south Wales are Leave supporters and Mr. Mann believes they will feel betrayed if the urban intelligentsia deprives them of Brexit.
Political pundits are still predicting Mrs. May will lose Tuesday's vote, which will almost certainly be followed by Labour calling for a vote of no confidence in her government.
Around 112 Conservative MPs have said they are going to vote against the government's deal, including Gareth Johnson, who resigned from the whips' office on Monday in order to vote with his conscience.
Mr. Mann said he was not sure if "Parliament and its authority will survive" if Britain ends up with either a no-deal Brexit or backs out of Brexit altogether.
"My voters will walk — they may not vote Tory, they may not vote Ukip, may not vote for me — they will walk and they'll say the political process is useless, it's broken, you're all to blame," he said in Parliament last week.
The PM met John Mann & other Labour MPs yesterday to discuss how to improve her deal. If the speaker accepts Mann's amendment on protecting and improving workers'/environmental rights it'd be astonishing if the govt didnt accept it —esp as todays debate focuses on those topics— iain watson (@iainjwatson) 10 January 2019
Former Labour minister Caroline Flint is backing Mr. Mann's amendment, as is another prominent northern Labour MP, Lisa Nandy, and Gareth Snell, MP for Stoke-on-Trent.