Conservative lawmaker James Duddridge on Wednesday called the Brexit negotiations "an absolute disaster" and said Johnson's speech had been "inspirational".
The pound dropped 0.4% on the day to as low as $1.2963, close to yesterday's three-week low of $1.2941, before recovering to $1.2990 later.
Her plea to unify behind "decent, moderate and patriotic" policies came a day after her rival and former foreign secretary Boris Johnson trashed her so-called Chequers plan for Brexit and challenged her authority, though he stopped short of declaring his intentions to be the next party leader.
When the Prime Minister did speak of Brexit, it was without referring once to her Chequers soft-Brexit plan by name, a sign that she has now accepted the term has now acquired a tox status. It will be a system that looks across the globe and attracts the people with the skills we need, she said.
"If we all go off in different directions in pursuit of our own vision of the flawless Brexit, we risk ending up with no Brexit at all", she said in a clear nod to euroskeptic MPs who have published their alternatives plan for leaving the EU.
May is urging her fractious Conservative Party to unite and help her seal a deal with the bloc.
He said that if the Chequers plan were adopted, "the United Kingdom will effectively be paraded in manacles down the Rue de la Loi", a Brussels street lined with European Union offices. And she will experience no voice malfunctioning issues either that would make it nearly impossible to watch or listen to what she is saying.
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These are meant to avoid such checks on the border between Northern Ireland and Ireland itself - something all sides want to avoid.
People are entitled to express their view at fringe meetings, he said, but predicted people would be "rallying behind" Mrs May when she delivers her speech.
To be fair: May is entitled to feel exasperation with the hand that she has been dealt, with her toxically fractious party and with the belligerent Brussels EU leadership, but when everything is said and done she knew what she was getting herself into.
And she signalled the growing threat to the party from Labour leader Jeremy Corbyn, whose policies calling for nationalization of railways and greater spending on social services have found growing support across the country.
She also took some subtle shots at Mr. Johnson, poking fun at a recent profane comment he made about business leaders by saying she also had a four-letter word for business - "back", as in "back business".
Britain's governing party is deeply divided over the country's impending departure from the European Union, with pro- and anti-EU camps both criticising the prime minister's negotiations with the bloc.
Britain will bring in a salary threshold for highly skilled workers' visas as part of its post-Brexit immigration system, interior minister Sajid Javid said on Tuesday.
■ On criticism of him from the chancellor: 'I want to congratulate my friend Philip Hammond for predicting that I will never become prime minister - it's the first treasury forecast in a long time, I think, to have a distinct ring of truth'. May out as leader, convinced there is no clear alternative and that Mr. Johnson isn't up to the job.