Boris Johnson has said the last three years under Theresa May will seem like a "bad dream" once he gets the UK out of the European Union.
The favourite in the Tory leadership race insisted he would stick to his commitment to deliver Brexit on October 31.
He also promised to tackle the social care crisis if he becomes prime minister, saying people should not be forced to sell their homes to pay for the support they need.
Mr Johnson used a Daily Express interview to again stress his commitment to leave the EU "come what may" on Halloween, with or without a deal.
But the scale of the task facing him was laid bare in the Commons on Thursday, as Cabinet ministers who expect to return to the backbenches under a Johnson administration put down a marker about their willingness to cause trouble.
MPs voted by a majority of 41 to back a measure aimed at preventing Mr Johnson suspending Parliament in order to force through a no-deal Brexit, with 17 Tories rebelling.
Chancellor Philip Hammond, Justice Secretary David Gauke, Business Secretary Greg Clark and International Development Secretary Rory Stewart did not take part in the vote.
All are expected to be on the backbenches under Mr Johnson and could be a thorn in his side as he struggles with a Tory-DUP majority which could be reduced to just three if the Conservatives fail to hold Brecon and Radnorshire in the August 1 by-election.
Mr Johnson insisted he could deliver the result of the 2016 referendum, claiming "the three years will seem like a bad dream".
"We'll get on with it and think much more about what we are going to do to unleash the talents and the potential of the whole country, that's what I want to do."
Mr Johnson has declared the Withdrawal Agreement reached by Mrs May and the EU "dead", meaning that any replacement would have to be negotiated by October 31 if the UK is to avoid a no-deal departure as he would not seek another delay if he becomes PM.
"Why would we have another extension? I don't think there is any appetite in the UK for another extension, nobody wants it. I certainly won't have it.
"And don't forget how it works – at the moment, the UK leaves legally on October 31, that is the law. The only way that can be prevented is if a UK prime minister were to ask for an extension.
"Well, I'm not going to ask for an extension."
On social care, Mr Johnson acknowledged the anxiety caused as a result of the current system.
"It is inequitable. Some families having to raise hundreds of thousands in order to pay for the costs of care, others are getting those costs met, or at least partly met," he said.
"There is a real sense of anxiety this is causing and we need to address it."
Either Mr Johnson or rival Jeremy Hunt will become prime minister on July 24, the day after the result of the Tory leadership contest is declared.
In an extraordinary indication of the resistance Mr Johnson might face if he attempts to push through a no-deal Brexit, the BBC reported that opponents could drag the Queen into the bitter political row.
According to BBC2's Newsnight, senior Tories have discussed using a parliamentary device known as a humble address to the Queen requesting her to act.
If passed, the motion would say that if the new prime minister ignored a vote rejecting no deal the Queen would be asked to exercise her right as head of state to travel to the next EU summit and ask for Brexit to be delayed.
But even rebel Tory ringleader Dominic Grieve played down the idea, telling the programme: "One of my duties as a Member of Parliament is to avoid drawing the monarch into politics."