Writing in his Daily Telegraph column, Mr Johnson said: “If we fail yet again, and kick the can down the road, we will continue to undermine trust in politics. If we say that it is not a ‘hard’ deadline, we will fuel the suspicion that there is a conspiracy by the elite to frustrate the will of the people.”
Mr Johnson and Mr Hunt are the final two candidates in the race to replace Theresa May and Brexit is top of the agenda.
The former London mayor has promised to take the UK out of the EU with or without a deal on Halloween, while the Foreign Secretary has admitted he would delay Brexit to strike an agreement.
The pair have been going head-to-head in hustings events across the country.
It is up to Tory party members to pick the next prime minister and the winner will be announced on July 22.
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8.25am update: Johnson will end public sector pay freezes – Health Secretary
Mr Johnson will do away with public sector pay freezes, Matt Hancock has said.
The Health Secretary said: “Now that there’s money available we need to show the public sector some love – they do a brilliant job for the country.
“People in the public sector need to be properly rewarded for the brilliant job they do.
“Higher pay, not higher taxes, means a pay rise for everyone, including in the public sector.”
Mr Hunt made enemies of the NHS in a row over new contracts for junior doctors in 2016.
8.15am update: Hunt unveils £20bn no-deal Brexit war chest
The Foreign Secretary will announce plans for a £20 billion war chest in the event of a no-deal Brexit.
Mr Hunt is set to unveil a 10-point plan for leaving the EU without an agreement.
The Tory hopeful is expected to tell supporters today: “You cannot leave the EU on a wing and a prayer. Britain deserves better.”