It came as Mr Johnson private life was again thrust into the spotlight, with the favourite to become the next Prime Minster declaring he was ready to “live with” question marks about his fitness to serve over the issue.

Mr Hunt attacked the SNP government at Holyrood, calling it “the most bullying, divisive, duplicitous, anti-business government that Scotland has ever seen”.

And both men said they would put the future of the UK before Brexit – but pledged to deliver both.

A pro-independence group protests ahead of the Scottish Hustings held by Jeremy Hunt and Boris Johnson in Perth. Picture: Jeff J Mitchell/Getty

The Foreign Secretary also took a swipe at the Scottish Government’s preparations for a “no-deal” Brexit, warning that not enough is being done north of the Border.

Ms Sturgeon has said she will ask the new Tory leader for authority to hold a second referendum on independence, as control over the constitution in the UK is reserved to Westminster. This has so far been ruled out by both Mr Hunt and Mr Johnson.

Scots Tory leader Ruth Davidson has said that if the SNP wins a majority at Holyrood in two years on a platform to stage a second referendum it should happen.

But asked directly about this prospect, Mr Hunt ruled even this out.

Conservative leadership candidate Boris Johnson greets supporters ahead of the Scottish Hustings in Perth

“I’ve made it very clear I’m a Unionist with every fibre in my being so if there is another request for another referendum, the answer will be a polite no,” he said.

“I’m a democrat and I remember that in that independence referendum, the SNP very clearly said that this would settle the outcome for a generation and I think they need to be true to what they promised the Scottish electorate, just as we are true to what we promised the British electorate in delivering Brexit.”

Mr Hunt pledged that he will work with the Scottish Government on issues like immigration to make progress in the country.

“I will engage fully, responsibly and generously with Nicola Sturgeon on everything that helps Scotland move forward,” Mr Hunt said.

“But I will not engage with her on the issue of independence which will take Scotland backwards.

“And I will certainly not engage with her on the issue of a second independence referendum which is not what the people of Scotland want.”

He added: “If she asks for a second independence referendum I will decline in the most British and polite way. But it will be a no.”

Mr Johnson also made it clear last night he would rule out granting a second vote on Scotland leaving the UK.

“My view is that we had a referendum in 2014, the people of this country were promised it was a once in a generation choice they would make,” he said.

“They were told it was a once in a generation promise, I don’t think there is any case for breaking that promise do you?”

Asked if this would be the case even under a “democratically elected majority” at Holyrood under the SNP, he added: “I see absolutely no case for having a second referendum in Scotland – I think it’s absurd.”

Mr Johnson was again challenged at a hustings about aspects of his personal life. Asked by a Tory member whether a good prime minister needed to be “a loyal husband and father”, Mr Johnson replied: “I think that on these sorts of things, I have been asked all sorts of questions in the last 20 or 30 years, and I just don’t comment on that stuff.

“What people in this country want to hear is what my plans are to get Brexit over the line, what I’m going to do to unite our country and the ideas I have for a fantastic agenda of modern Conservatism.”

The female Tory member who asked the question said that his refusal to answer meant voters would “come to their own conclusion and it may not be a favourable one”.

Mr Johnson said: “Then I’m going to have to live with that.”

Mr Hunt had made it clear earlier in the day he did not underestimate the threats to the UK after Theresa May warned the previous day in Scotland her successor must seek to protect it.

He added: “I do think we need to take the threats to the Union very seriously – I think it’s the most precious thing about our country.”

The Conservative leadership candidate said a no-deal Brexit could change the situation on independence and made it clear he did not think enough was being done to prepare for a no-deal scenario in Scotland.

“All of us have to do more but to date as I’ve been watching the no-deal preparations I would like to see more focus on that from Nicola Sturgeon,” he said.

“[The Scottish Government] have been very disappointing in their preparations of a no-deal Brexit, which none of us want, but any responsible government or authority in the United Kingdom should be taking seriously because there is that risk.”

Questioned what more the Scottish Government should be doing, he said: “This isn’t the time to go into details but I think they know, and we know, the areas where more can be done.”

Questioned if a no-deal could change the situation on independence, the Foreign Secretary said: “If it’s handled the wrong way, yes.

“But I’m going to make sure if we do end up with a no-deal Brexit that it’s one where we leave no stone unturned in order to mitigate the impact for businesses affected by Brexit whether north or south of the Border.”

SNP Westminster leader, Ian Blackford hit out at the “high-handed arrogance” over a second referendum.

He said: “The people of Scotland overwhelmingly voted against Brexit – yet we face being driven off an economic cliff-edge by a Tory government which we have also overwhelmingly rejected. This high-handed arrogance from Jeremy Hunt may appeal to the Tory faithful but it certainly won’t appeal to the rest of Scotland. No wonder support for the Tories has plummeted in Scotland.

“The mandate to hold another independence referendum is not a matter of opinion – it is a matter of fact.”

Scottish independence: Tory leadership contenders raise IndyRef2 stakes