A national "Let Us Be Heard" demonstration will take place October 19 in London, supported by the People's Vote and calling on Johnson to secure a Brexit deal that British voters will then approve or reject.
"I really don't see how we can have a situation in which the British ability for negotiation is absolutely torpedoed by Parliament in this way, with powers of the British people handed over to Brussels so that we can be kept incarcerated in the European Union without that actually being put to the people in a form of a vote".
Mr Gauke was one of 21 MPs to be deselected by the Conservative Party after rebelling against in the Commons this week. "I don't want an election at all, but I can't see another way".
Jo Johnson had been a member of Parliament for Orpington, a district on the southeast of London, since 2010.
Police surround Brexit protesters as Prime Minister Boris Johnson visits West Yorkshire after promising to recruit an extra 20,000 police officers.
Cummings, architect of the "Vote Leave" campaign in the 2016 Brexit referendum, is Johnson's top advisor and de facto chief of staff.
Universities minister Jo Johnson, brother of Prime Minister Boris Johnson has resigned as an MP and minister.
The PM's continued campaigning comes after a day of unwelcome events saw Jo Johnson quit as a senior minister attending meetings of his brother's Cabinet.
Conservative MP Philip Lee also defected on Tuesday, joining the Liberal Democrats in the House of Commons as the prime minister was speaking and leaving Johnson with a minority. Under this plan, Brussels would decide how long the United Kingdom stayed in the EU.
Major, Conservative prime minister from 1990 to 1997, said lawmakers' service now seemed to be worthless unless they were "parroting the views of a prime minister influenced by a political anarchist", a reference to Cummings.
Johnson again attacked Labour leader Jeremy Corbyn for opposing the call for an election, saying he had been demanding an election for several years.
Asked if Brexit would happen on October 31, Johnson's belligerent senior adviser, Dominic Cummings, a focus of many departing Conservative lawmakers' grievances, told Reuters: "Trust the people". "I think it's a no-brainer".
The sense that the prospect of a "no-deal" exit had receded pushed the pound 1.4% higher on Wednesday and it surged to a five-week high on Thursday, ending at $1.2317.
He's taken a tough stance on those from his own Conservative Party who voted with the opposition in a bill created to make sure that Britain doesn't leave the European Union without a deal - they've been sacked. UBS Global Wealth Management said sterling could rally to $1.30 if Brexit was delayed until January 2020 and an election was held after October.
The bill is now with the House of Lords, which has committed to passing it before Friday, September 6.