The PM thanked the former Brexit Minister David Davis and former Foreign Secretary Boris Johnson for their work.
"I want to recognize the work of the former Secretary of State for Exiting the European Union for the work he did to establish a new department and steer through Parliament some of the most important legislation for generations," Mrs. May told the MPs.
"We do not agree about the best way of delivering our shared commitment to honoring the result of the referendum" voters approved to leave the EU, the PM said.
She also marked the resignation of the Foreign Secretary Boris Johnson, announced mere minutes ahead of her speech in the parliament on Monday.
The PM recognized "the passion the Foreign Secretary demonstrated in promoting a global Britain to the world as we leave the European Union."
The Right Brexit
On July 6, Mrs. May and her senior ministers reached an agreement on Britain's policy regarding the future trade relations with the European Union. However, in just two days, the Brexit Minister said he didn't believe in the government's vision for the EU-UK relationship, as he resigned on July 8. He said the government's plan "would be a risk at least of delivering a poor outcome," adding that Britain was "giving too much away, too easily."
In her parliamentary address on Monday, Mrs. May defended her post-Brexit trade plan and said it was the only way to avoid hard Irish border. The PM called the government's EU exit plan 'the right Brexit' and urged the European Union to back it.
The published Brexit paper also said the UK government "would strike different arrangements for services, where it is in our interests to have regulatory flexibility, recognizing the UK and the EU will not have current levels of access to each other's markets."
Commenting on that statement, the PM told the Parliament:
"We believe it is important to maintain more flexibility in how we're dealing with services. On services, we want to be free to ensure that we are able to put in place what we believe is necessary to maintain our key position in services, not least on the financial services."
The UK government must prepare for a range of outcomes including a ‘No Deal Brexit,' the PM said, adding that the preparations for it will be stepped up.
Support & Opposition
Commenting on May's speech, the Chancellor of the Exchequer Phillip Hammond backed the PM, confirming his full support.
The leader of the opposition Jeremy Corbyn criticized Theresa May and her Cabinet for inability to broker a good deal with the European Union.
"Two years of soundbites, indecision and Cabinet infighting, culminating in a series of wasted opportunities with more and more people losing faith this government is capable of delivering a good Brexit deal and that is just within her own Cabinet. Two years from the referendum, 16 months from the Article 50 being triggered, it is only this weekend the cabinet managed to agree a negotiation position among itself and that illusion lasted 48 hours," Mr. Corbyn told the Parliament.
"We have a crisis in government, two Secretaries of State have resigned and still we are no clearer on what future relationship with our nearest neighbors and biggest partners will look like," he added.
The PM reacted to Corbyn's words with laughter and reminded him that his own administration went through "103 resignations from his front bench."
"I'll take no lectures from the right honorable gentleman," Mrs. May concluded.
Davis' and Johnson's resignations dealt a significant blow to Mrs. May's leadership, with rumors of a no confidence vote circulating among British officials.
Asked whether Mrs. May would contest any vote on a confidence motion in her leadership, her spokesman said: "Yes."