Theresa May has insisted her Cabinet is "united" behind her vision for Britain, despite renewed feuding over Brexit as the Conservatives' annual conference opens in Manchester.

The gathering has already seen an incendiary intervention by Foreign Secretary Boris Johnson, who laid down a raft of red lines for EU withdrawal including an insistence that a transition phase must not last "a second more" than two years.

Mrs May sidestepped the question of whether Mr Johnson was "unsackable" in a high-profile TV interview, saying only that the Foreign Secretary was "absolutely behind" the plan for Brexit which she set out in a speech in the Italian city of Florence last week.

She also declined to answer whether she would resign as Prime Minister if she fails to secure a Brexit deal with the European Union and the UK crashes out without agreement on a future relationship in 2019.

The PM told BBC1's Andrew Marr Show: "What I have is a Cabinet that are united in the mission of this Government, and that is what you will see this week."

Mrs May said she plans to say sorry to activists for the party's performance in the snap election she called earlier this year, when she addresses the Conservatives' national convention on Sunday.

But asked whether her decision to call the poll three years early was a "mistake", she replied: "No. Is it ever a mistake to give people the opportunity to vote? I don't think so."

mfl As delegates arrived in Manchester, a post-mortem of the June 8 poll by former minister Sir Eric Pickles called on the Tories to do more to attract young voters and members of ethnic minorities.

The Pickles report also called for a formal committee of senior ministers and officials to draw up the manifesto, to prevent a repeat of complaints that the 2017 platform was drawn up secretively by Mrs May and a close inner circle including advisers Nicholas Timothy and Fiona Hill without consultation on key policies like the so-called "dementia tax".

Mrs May kicked off the conference with a concerted push for the youth vote featuring a university tuition fee freeze and a £10 billion boost for first time buyers.

Attempting to shift the focus from Brexit to a good news domestic agenda, Mrs May announced that tuition fees will be frozen at the current £9,250 level until 2019, rather than increase with inflation by £250.

Under Mrs May's plans, the amount graduates can earn before making student loan repayments will also rise from £21,000 to £25,000.

The figure will then increase in line with earnings after next year, with the Tories saying the package will produce a saving of £360 in 2018/19 for graduates earning at least £25,000.

In a bid to help young people get on the housing ladder, Chancellor Philip Hammond is announcing a £10 billion expansion of the Help to Buy: Equity Loan scheme in order to aid 135,000 new purchasers.

Mrs May told Marr that the message she took from the election was that Tories need to "listen to voters", who appeared to feel "even more keenly" than she had realised the pressures which she identified when she came into power promising to help the "just about managing".

She said that the sources of funding for the new policies would be set out at Mr Hammond's Budget on November 22.

"What is important in the announcements we have made today is that we have listened to what people said in the general election and we recognise that there are key areas we need to address," she said.

Asked if she had lost authority over her ministerial team, Mrs May insisted the Cabinet were "united in a mission to build a country that works for everyone and agreed on the approach that we take in Florence".

She added: "I had a Cabinet meeting before my Florence speech and everyone was agreed that the position the United Kingdom was taking was absolutely the right one. We are going forward on that basis.

"Boris is absolutely behind the Florence speech and the line that we have taken. What Boris is saying is the importance of the approach we have taken in the Florence speech. That has moved the discussion on and created a momentum in the negotiations."

Asked if Mr Johnson was "unsackable", Mrs May replied: "Let's be very clear about what we have here in this Government. We have a Government that is determined to build a country that works for everyone..

"You talk about Boris's job, you talk about my job. I think the people watching this programme are actually interested in what we are going to do for their jobs and their futures and their children's futures."

Mr Johnson's Brexit comments came a day after he ramped up pressure on Mrs May to deliver higher pay rises for public sector workers.

And he sparked fury among some Conservatives by participating in a Channel 4 documentary due to air on Sunday in which a friend is reported to have said he believes Mrs May has "a year at most" to remain in Downing Street.

His interventions drew a stern rebuke from former education secretary Nicky Morgan who told the Independent: "Those who are pushing this agenda have no place in a responsible government - it is a dereliction of their duty to act in the national interest. And it has to stop."

Scottish Conservative leader Ruth Davidson also entered the Tory fray, calling for "serious people" to take charge of the Brexit process.

Remain-backing Tory MP Anna Soubry said on Twitter: "People are fed up with Tory wars and Brexit mixed messages. Boris Johnson must grow up or go."

Mrs May, who celebrates her 61st birthday on Sunday, made it clear she intends to remain in power.

She told the Sunday Telegraph: "I will fight the next election. I'm not a quitter, I'm in it for the long term and I believe there is a long-term job to do."

The comments came as the Observer reported that Communities Secretary Sajid Javid declined to reply when asked if Mrs May should lead the Tories into the next election.

Mr Javid laughed when asked the question, then stood up and declared "I think we are out of time," the newspaper said.

As speculation over Mrs May's future continued, Mr Hammond dismissed claims that he had offered his backing to Mr Johnson for a leadership bid as it became clear the Tories had lost their Commons majority.

Mr Hammond told the Mail on Sunday reports that he texted the Foreign Secretary at 4am on the morning after polling (Friday June 9) to express support for Mr Johnson when it looked as if the PM might have to resign were not true.

Tory party chairman Sir Patrick McLoughlin said there was always "chitter chatter" about the leadership at conference time but Mrs May was a "strong leader and is the right person to take this country forward" and lead the Brexit talks.

Asked about reports that Mr Johnson believes Mrs May has "a year at most" left in the job, Sir Patrick told LBC Radio: "I have not seen Boris's comments. If he said that I don't think that's right. I think she is the person that is right for the Brexit negotiations, which are very important."

mfl Mr Javid later insisted he backed the PM to lead the Tories into the next election despite dodging the question in his Observer interview.

He told Radio 5 Live's Pienaar's Politics: "The answer is yes. If she, Theresa May, decides to, as she has said, if it's her view she wants to keep leading the party, and that would be, I think, welcomed by many people, if that is what she decides to do, I will back her. I would support her.

"And I think that is the view of many people that she is the right person to be leading this country forward."

mfl Speaking to Marr, Mrs May defended the reforms to the student finance system - and refused to rule out moving to a graduate tax system in future.

Critics of the reforms have pointed out that the changes will still leave students tens of thousands of pounds in debt and the change to repayment thresholds will save graduates around £1 a day.

The Prime Minister said when the fees were hiked it had been expected that there would be a "diversity in the system" rather than most universities charging the maximum amount of fees.

Asked if there could be a graduate tax instead of the current system, she said: "By looking at it again we will be looking at the issues that people are raising, we will be looking at where the system has worked, we will be looking at the concerns that people have."

She warned a Labour government would result in a run on the pound and an economy "going into freefall" as she was challenged about her own stewardship of the economy.

Mrs May said getting a "successful future" after Brexit was one issue that needed to be addressed as she promised a "balanced approach" to the nation's finances.

That meant being "careful" with the public sector finances while ensuring that "across the whole of the country people are seeing the benefits of free trade, the benefits of the free market economy".