Mr Johnson said his role as transport minister had caused him concern about the impact of a no-deal outcome.
Walker said he did not think a disorderly Brexit was likely, but he added that if it did come to that the rights of European Union citizens in Britain would be protected.
"I mean volley to the left of the them, volley to right of them, and the Prime Minister charges on into the valley of death".
The ministers have proposed that Britain continue to pay European Union membership fees up to 2021 and follow the bloc's rules to avoid a cliff edge exit when it leaves in March 2019, the Sun said.
"While we wait to negotiate trading terms, the rules of the game will be set exclusively by the EU".
"And thank God Jo has come out today with a bit of sanity".
Mr Johnson's sister Rachel said she was "hugely proud" of her "honourable and principled brother Jo who has put the interests of the country ahead of his political career".
His older brother Boris resigned in July to protest May's Brexit plan - but Boris did so as a staunch support of a hard-line Brexit, while Jo Johnson backed the "remain" side during the June, 2016 referendum.
Speaking to Matt Frei, Stanley Johnson reiterated that Jo resigned because the government is not delivering Brexit and because he can not support the Brexit plan "in honesty".
Gross domestic product climbed 0.6pc in the third quarter, in line with analysts' expectations and up on growth of 0.4pc in the second quarter, the Office for National Statistics (ONS) said in an initial estimate.
Johnson published an online article saying he will not vote for the deal May is likely to bring back to parliament within weeks but he would campaign for a second referendum on Brexit. "My priority is really just to do my best as a now backbench MP to try and encourage the country to pause and reflect before we do something that is irrevocably stupid", Johnson said.