"We said we would and we haven't and the people think we're incompetent, so we need to get on with it".
Gareth Snell said he should have backed the agreement when it was put before the Commons for a third time, adding he would support a deal in future.
Pro-EU lawmakers say they will try to block a no-deal Brexit, though the House of Commons on Wednesday narrowly rejected an opposition attempt to legislate against it.
Johnson has said that he will deliver on the result with or without a Brussels deal.
Johnson has a chequered history, arguably known more for his gaffes and jokes than his achievements both as mayor of London and foreign minister.
Also on the programme - a question of gender and sex.
"Now is the time to unite this country and unite this society", he said, stressing that this task can be only achieved after leaving the EU.More news: Trump says he is ‘a little bit concerned’ about massive defense merger
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May has delayed Brexit twice - most recently to October 31 - as she tried and failed to get her divorce deal through parliament.
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". Mr Hancock replied saying "I think it's true, you can see by those things he's defended, the symbols that he's defended", adding that the Labour leader had defended a mural in East London which was anti-Semitic. "If he continues like this he will lose the trust of his MPs, he will lose the trust of the members of the Conservative Party, and ultimately the trust of the electorate".
The victor should be in Downing Street in late July.
He warned failure that to honour the referendum vote risked handing power to Jeremy Corbyn and Labour at the next general election.
He promised to provide the "clarity" of vision needed to deliver the result of the European Union referendum with or without a deal, and warned MPs they would face "mortal retribution" from voters if they tried to stop Brexit.
There is a chance that in a repeat of previous year, the MPs could try to take control of the Commons timetable on June 25, allowing them to introduce a law that might stop "no deal".