Scrambling to plot an orderly path out of the Brexit maze just days before the United Kingdom was due to leave on March 29, Mrs May rushed to Strasbourg - the home of the European Parliament - to secure additional assurances from European Commission President Jean-Claude Juncker.
It had been as high as $1.3290 earlier in the session on hopes British Prime Minister May would eventually secure a deal before Brexit in less than three weeks.
A DUP MP meanwhile told HuffPost UK that the deal remained "unpalatable" and Cox's legal advice "killed it dead".
Speaking in the House of Commons as May announced the agreement, Cabinet Office minister and her de-facto deputy David Lidington said MPs would face a "fundamental choice" later today "to vote for the improved deal or to plunge this country into a political crisis".
May said documents to be added to the deal provided "legally binding" assurances that the backstop would be temporary and that Britain would have a way to get out of it if the European Union failed to negotiate in good faith.More news: Teddy Bridgewater set to meet with Dolphins
After two-and-a-half years of haggling since the 2016 Brexit referendum, Juncker cautioned that this was the last chance for Britain.
Nick Boles, a leading Conservative pushing the government to rule out a no-deal Brexit, warned May that she would "forfeit the confidence of the House of Commons" if she failed to put it to a vote. "The PM is giving us basically the same deal", said Labour's shadow Brexit secretary Kier Starmer, who is calling for a "pause" and more time to consider the next steps.
It would also raise the possibility of a delay to Brexit, with further votes on leaving without a deal and postponing Britain's departure date set for later in the week if May's deal falls.
According to Cox, the interpretive document offered by the European Union would grant no legally guaranteed right to exit the Irish Backstop in the event of a deal deadlock and triggered some aggressive selling pressure around the British Pound.
Brexit will pitch the world's 5th largest economy into the unknown and many fear it will divide the West as it grapples with both the unconventional US presidency of Donald Trump and growing assertiveness from Russian Federation and China.More news: Militao: new Real Madrid signing
Supporters of Brexit argue that, while a "no-deal" divorce might bring some short-term instability, in the longer term it would allow the United Kingdom to thrive and forge beneficial trade deals across the world.
Ranko Berich, head of market analysis at Monex Europe, said: "we are now back to a base case where May's deal is rebuffed and she is forced to seek an extension".
"The backstop is an insurance policy, nothing more, nothing less". These had equal legal force with the withdrawal agreement, he claimed.
After Geoffrey Cox's advice, the DUP will take their own legal advice before deciding whether to back the deal.More news: 'Empire' Actor Jussie Smollett enters not guilty plea