"We should not and need not be stampeded by anyone", Johnson said.
Accusing the Government of "dithering" over its Brexit negotiations, he said that a "fog of self-doubt" had descended on Mrs May's stance to European Union withdrawal since she first set it out in a speech at Lancaster House past year. Britons should be "great independent actors" on the world stage, not "rule takers", he said.
The pound traded flat against the dollar and the euro on Monday ahead of a debate in parliament that could reveal significant dissatisfaction within British Prime Minister Theresa May's party over her plans for Brexit.
Johnson, warned today that the Brexit "dream is dying" and Britain is "headed for the status of colony" with May's plan to stay close to the EU.
At heart of this political saga is the fact that the politicians leading the Brexit "Leave" campaign - Boris Johnson chief among them - never actually explained to the British public what a vote for "Leave" entailed.
"This could lead to a damaging and disorderly Brexit because without this Bill passing we would not be able to retain the benefits of more than 40 existing trade arrangements; and neither will we have the means to protect consumers, industries and workers from being undercut by unfairly traded goods in a post-Brexit Britain", she said.
He argued that the problem was not that Britain had failed to make the case to Brussels for an ambitious free trade deal, but "we haven't even tried".
An accidental Prime Minister, stuck with a job that she did not choose for herself, May is faced with the dual task of negotiating with the European Union while at the same time not deviating much from the ultimate objective of Brexit for which almost 52% of the British population had given their nod.
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"Not the democratic disaster of ongoing harmonisation with no way out and no say for the UK".
The Daily Telegraph reported more than 100 MPs had joined the group - more than double the 48 needed to submit letters of no confidence in the Prime Minister to force a leadership contest.
And what will be viewed as a call to arms among his Brexiteer colleagues on the backbenches, Mr Johnson demanded Mrs May return to the proposals she set out in her Lancaster House speech in January 2017. "I am going to fight for our Brexit deal because it is the right deal for Britain".
Prime Minister Theresa May faces potentially highly damaging attacks from both sides in parliament this week over plans for Britain's future trading relationship with the European Union after Brexit.
He added: "Having examined the Chequers agreement".
Pro-EU Tory Phillip Lee, who quit as a minister over Brexit, condemned any thought of an earlier break as "shameful" at a "crucial time".
"The only solution is to take the final Brexit decision out of the hands of deadlocked politicians, away from the backroom deals, and give it back to the people", she said in an article for The Times. "I have come to the conclusion that.it is not what people voted for".