Shortly after the article was published online, Scottish Conservative leader Ruth Davidson tweeted: "On the day of a terror attack where Britons were maimed, just hours after the threat level is raised, our only thoughts should be on service". "All behind Theresa for a glorious Brexit".
Johnson's article - which will likely reignite speculation among top Tories of his leadership ambitions - comes less than a week before Theresa May is due to give a pivotal Brexit speech in Florence.
Mr Johnson's future in the Cabinet has come under question after he set out a detailed vision of Britain's post-Brexit future that has been viewed as a challenge to Theresa May's leadership.
Corbyn, meanwhile, said Johnson's comments on the "fantasy" £350m figure was another attempt to "mislead the British public".
"As we prepare to leave the European Union it is therefore vital that we agree a new way to ensure continued security, law enforcement and criminal justice cooperation", she said.
"I know what an irrepressible enthusiast (Johnson) is about Brexit, and what he's done is set it out there, I think it's absolutely fine, I would expect nothing less from Boris", she said.
Johnson's renewed claim that £350m would be saved to spend on the NHS, which even featured on the side of a Leave campaign bus, was shouted down by Remain campaigners a year ago who accused Leave of misleading the public.
First Secretary of State Damian Green, effectively May's deputy, told Sky News on Sunday that Johnson will not lose his job over his intervention or its timing.
May's deputy, Damian Green, said also weighed in on Sunday, saying that Johnson had written a "very exuberant" article but it is "absolutely clear to everyone that the driver of the auto in this instance is the prime minister".
Looking to the future, Johnson said Britain would not expect to pay for access to European Union markets any more than the European Union would expect to pay for access to British markets.
A Government spokesman said: "We believe that the negotiations on the future partnership should begin as soon as possible". It will suggest that the fight against crime and terror could be underpinned by a new security treaty between the United Kingdom and the EU.
Last month, EU Chief Negotiator Michel Barnier also warned that Britain would be forced to leave Europol and that the EU-UK split would weaken British security and counter-terrorism. "They (the EU) want the same outcomes".
"The PM has expressed the bald truth which is that we need to have this agreement - they do and we do - and we will get it".