Johnson will join a lengthy list of leadership rivals, most of whom have already launched their bids.
He commented: "I don't think there's a credible way that you can leave with a deal on October 31".
The People's Vote campaign, which includes several pro-EU groups, plans a series of rallies around Britain over the next few months called "Let us be heard".
"I am not aiming for a no-deal outcome", said Mr Johnson, a 54-year-old former foreign minister.
He acknowledged that his use of language - such as his description of Muslim women who wore the burka as letter boxes - sometimes resulted in "some plaster coming off the ceiling".
Also on the programme - a question of gender and sex.
Speaking in the Commons, Snell said ceramics firms asked him "time and time again" to back a deal so they could make preparations for the future while food manufacturers wanted him to make a decision so they could "get past stockpiling".
"Any Tory leadership candidate should know that Parliament will continue to fight against no deal".
Officially launching his campaign on Wednesday, Javid highlighted the racial barriers he had to surmount as a child of Pakistani immigrants, recalling racial abuse in school and being told that "my face didn't fit".
"I understand why they're saying it about leaving on October 31 deal or no deal but I think it's a mistake".
The 313 Conservative MPs will whittle down the field to two by June 20, and that pair will then be put to a ballot of around 160,000 Conservative party members.
But, if they can not break the political deadlock in parliament, a general election may be inevitable.
He warned failure that to honour the referendum vote risked handing power to Jeremy Corbyn and Labour at the next general election.
Never one to hold back, Johnson warned Wednesday that if politicians delayed Britain's European Union departure again, "we will reap the whirlwind and we will face mortal retribution from the electorate".
In the Commons, the cross-party motion which would have enabled MPs to take control of the business of the House on June 25 was defeated by 309 to 298 - a majority of 11.
In his speech, Mr Javid said the new Tory leader must understand "what we have done wrong as a party and as a Government".