Speaking on BBC Radio 4's Today programme, he said the balance of the House of Commons was a "limiting factor" to what the United Kingdom could propose, as was the need of business for frictionless trade across borders.
"There was always going to be a moment in time that was needed for the British Prime Minister to show her authority because she had a very divided cabinet on her approach to Brexit".
"How are we as an industry or indeed the civil service to take the government seriously when they say that housing is a priority when, in fact, they play "Fantasy Housing Minister League" like this with scant regard for the consequences."
If May survives the domestic political turmoil, she still has to convince European Union leaders that her proposals can work.
They were announced less than an hour before May was due to face the press alongside German Chancellor Angela Merkel at an worldwide summit in London.
Mrs May was speaking amid speculation over further possible resignations of Leave-backing Tories, following the loss of three ministers, two party vice-chairs and two parliamentary aides over the course of 48 hours. "It should be a chance to do things differently", adding "that dream is dying, suffocated by needless self-doubt".
Earlier, Downing Street announced Johnson's resignation as foreign secretary, just minutes before May addressed MPs about the softer Brexit plan agreed at Chequers on Friday.
If Davis's resignation rattled May, Johnson's shook the foundations of her government.
This could mean Brexit being delayed, a change of government or a second referendum, he said.
May's personal authority was badly damaged after she called a snap election previous year to strengthen her hand in Brexit talks but instead she lost her parliamentary majority meaning she has to rely on a small Northern Irish party to govern. He was housing minister before taking up the top Brexit job.
But others argued May had adopted the most realistic plan after she was weakened in an ill-judged election a year ago when she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern.
"The biggest problem Theresa May now faces is selling this complex and nuanced proposal to her MPs and the British public", he wrote in an article for The Guardian.
"Now there is chaos", the paper said in its editorial.
The new Brexit Secretary has been urged to highlight the importance of agriculture in future Brexit negotiations with the EU. "Brexit must and will happen".
The major issues for Britons were concerns about immigration, sovereignty and the sums paid to the EU. He says the Brexit "dream is dying, suffocated by needless self-doubt", and that Britain is "headed to the status of a colony", having to swallow European Union writ without "any ability to influence these laws as they are made".
A minister quoted the prime minister as saying, "If we don't pull together, we risk the election of Jeremy Corbyn as prime minister", The Guardian reported.
In his resignation letter, Johnson said: "On Friday, I acknowledged that my side of the argument were too few to prevail, and congratulated you on at least reaching a cabinet decision on the way forward".
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