Foreign Secretary Mr Hunt said he was “delighted” to have come second, saying: “This serious moment calls for a serious leader.”
And Environment Secretary Mr Gove said it was “all to play for” and he was “very much looking forward” to the TV debates on Channel 4 on Sunday and on BBC One on Tuesday next week.
Home Secretary Sajid Javid said: “I look forward to continuing to share my positive vision and my plan for uniting the country.”
Health Secretary Matt Hancock thanked his supporters, saying it was “terrific to have more votes from colleagues than I could have hoped for”.
Former Brexit secretary Dominic Raab, said he was “proud and honoured” and he had a “good base to build on”.
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Media captionRory Stewart: “I don’t look anything like the previous PM”, and he negotiates “in a completely different way”.
International Development Secretary Rory Stewart told the BBC’s Politics Live he was “completely over the moon” to have got through the first vote.
He said he only had six declared votes ahead of the poll, but “more than three times that” voted for him in the secret ballot.
So is the Boris Johnson bandwagon unstoppable?
It’s worth remembering that the leading candidate at the same stage in the Conservative leadership contest in 2005 was David Davis…who went on to lose.
And in 2001 it was Michael Portillo, who then failed to make the final two.
So opponents of Mr Johnson could still gang up and do him in.
But as one canny Conservative observer put it: “Backing Boris is the ambitious thing to do.”
By being so far in front, MPs who want to climb the ministerial ladder may try to board the bandwagon now.
But his relatively rare media appearances means that, presumably, the former foreign secretary recognises that he can be his own worst enemy.
His long-standing ally Conor Burns tells me he takes nothing for granted.
Mr Johnson carries his lead like an impressive yet fragile precious vase – his opponents will be hoping if they can’t trip him up he will fall over his own feet.
But on Brexit especially his detractors cannot unite around a single alternative vision – and that may be his best hope of avoiding disaster.
Justice Secretary David Gauke said Mr Stewart was now the main challenger to Mr Johnson, saying: “He’s really in with a chance and the momentum is with Rory.”
But Defence Secretary Penny Mordaunt, who is supporting Mr Hunt’s campaign, said the foreign secretary is “attractive to many sides of the party because he’s a serious individual”.
And Schools Minister Nick Gibb told BBC Radio 4’s World at One that Mr Gove was now “best placed as a Brexiteer to challenge the front runner” Mr Johnson in the final.
The UK’s next prime minister
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Mr Harper said he continued “to believe we need a credible plan that delivers Brexit” in order to “restore trust”.
Mrs Leadsom’s campaign team said they were “disappointed” but “wish all the other candidates well”.
And Ms McVey said she was “extremely grateful” to those who had voted for her in the ballot.
Subsequent ballots are scheduled to take place on 18, 19 and 20 June to whittle down the contenders until only two are left.
The final pair will then be put to a vote of members of the wider Conservative Party from 22 June, with the winner expected to be announced about four weeks later.
TV debates ‘important’
TV election debates are also scheduled to take place with the leadership candidates, but not all have confirmed they are taking part.
Work and Pensions Secretary Amber Rudd, who is backing Mr Hunt, urged all the candidates to take part, saying the Conservative Party “needs to remember that we’re not just choosing a leader, we’re choosing a prime minister and the public need to see them”.
And former Brexit Secretary David Davis, who is backing Mr Raab, said it was “very important” that the contenders participated in debates.
Mr Johnson has previously been criticised by some of his rivals for not taking part in media interviews during the campaign.
The leadership race has so far been dominated by Brexit and arguments over whether a deal can be renegotiated with the EU by 31 October, and whether talking up a no-deal Brexit is a plausible promise.
Compare candidates’ policies
Select a topic and a candidate to find out more
BREXIT
– Has said he would consider a further delay to Brexit to achieve a better deal. – Plans to negotiate a “fullstop” to the Irish border backstop plan. He wants a free trade agreement, similar to the deal between Canada and the EU. – Would support a no-deal Brexit if he couldn’t get a better deal from Brussels.
– Says leaving with no deal is not an option, so it’s between leaving with a deal and not leaving at all. – Five-point Brexit delivery plan would include setting up an Irish Border Council with £1bn invested to develop a new system and time-limited backstop in Ireland. – Proposes negotiating a comprehensive free trade agreement, which would involve leaving the single market and customs union.
– Would leave the EU with no deal, but it’s not his preferred option. – Wants changes to the Irish backstop and proposes sending a new negotiating team to Brussels. – Wants to make changes to the Withdrawal Agreement and thinks it’s possible to get them done by 31 October, but has not ruled out an extension.
– Would focus on making changes to the backstop. Would commission UK border force to work on solving the Northern Ireland border problem, paid for by the UK. – Says he cannot envisage circumstances in which he would want to have another extension to the UK’s exit date and the country must be prepared for a no-deal Brexit.
– Wants to leave on 31 October, the deadline for Brexit set by the EU, with or without a deal. He admits a no-deal exit will cause “some disruption” but says the “way to get a good deal is to prepare for no deal”. – Wants to remove the backstop from any deal and replace it with “alternative arrangements”. – Says he would withhold the £39bn “divorce” payment the UK is due to give the EU as part of the negotiated deal. He says the money will be retained until there is “greater clarity about the way forward”.
– Wants to re-open the withdrawal agreement for renegotiation in order to “overhaul the backstop”. – Says a new deal would include “the vast majority” of the deal Theresa May negotiated, but would replace the Irish backstop with “alternative arrangements” involving “advanced customs and trade measures” and checks away from the border. – Willing to leave on WTO rules, claiming it is “far better than leaving with a fatally flawed deal”, and will not rule out proroguing Parliament (essentially shutting it down) ahead of the 31 October deadline to prevent it blocking a no-deal Brexit
– Believes a no-deal Brexit would be “catastrophic” for the UK and is “undeliverable” and “unnecessary”. – He said it was unrealistic to believe the UK could get a new Brexit deal agreed by the EU and Parliament by the 31 October deadline.
TAX AND SPENDING
– Says he wants to replace VAT after Brexit with a lower, simpler sales tax. – Wants to create the “most pro-business” tax regime in the world and put business at the heart of the revival of Britain. – Says he would not use the tax and benefits system to give the already wealthy another tax cut. – Says he would scrap the High Speed rail 2 project.
– £5bn economic stimulus into the economy paid for by reducing rate of debt repayments. – Plans to introduce an Amazon Tax for social media platforms and other tech giants. – Proposes increasing the National Living Wage to £10.21 by 2022.
– As an entrepreneur, he wants to turn Britain into the next Silicon Valley, a “hub of innovation”. – Pledged to slash business taxes to the lowest in Europe to attract firms to Britain after Brexit and reduce corporation tax.
– Has promised to break from the austerity of the past nine years by slowing the pace of debt reduction. – Says this would free up about £25bn a year for spending priorities, including education. – Other money would be spent on local government and efforts to tackle crime, including an increase in the number of police officers by 20,000.
– Pledges to cut income tax for people earning more than £50,000 by raising the 40% tax threshold to £80,000. – Says it will benefit three million people and would cost £9.6bn a year. – Plans to pay for the cut partly from a pot set aside by the Treasury for a possible no-deal Brexit, and partly by increasing employee National Insurance payments.
– Wants to cut the basic rate of income tax from 20% to 15%. He suggests the basic rate falling by a penny a year. – Would equal a tax cut for the majority of UK workers. HMRC says there are currently 26.3m basic rate tax payers, but IFS says it costs about £5bn for every 1p cut in the rate of income tax. – Wants to raise the point that people start to pay national insurance to be the same as income tax, £12,501 a year. – This is expected to cost £10bn a year.
– Criticises other candidates for offering “cheap electoral bribes” to win support. – Says rather than being “straight” with people, his opponents have pledged “eye-watering” tax cuts worth £84bn.
HEALTH AND EDUCATION
– Says he wants to ensure the NHS is “fully-funded, properly funded” and that funding is protected under law. – Says he will spend £1bn extra on schools if he becomes prime minister.
– Says supporting mental health would be front and centre of his government’s policies, from supporting veterans in the MoD to promoting physical activity in DCMS. – Freedom of movement for qualified doctors and nurses from around the world. – £3bn over five years for primary and secondary school pupils, an extra £400 for every child, and address the funding formula.
– Mental health support in every school and a crackdown on social media companies that fail to regulate their content. – A cut in interest rate paid on tuition fees. – Long term plan to provide more funding for the teaching profession in return for a guarantee that no one leaves the education system without a “rigorous qualification” sufficient to work up to at least the average salary.
– Has suggested slowing down the rate of debt reduction, to release money for education. – Wants to see a “multi-year, multi-billion-pound boost” to spending on schools to “change the life chances of so many young people”.
– Promises to raise spending on secondary school pupils to £5,000 each. – Called the funding gap between some schools in cities compared to those in rural areas a “disturbing reality”. – Has previously said money spent on the EU could be put into the NHS.
– Wants review of spending in Whitehall, with a “special commission” to look at public sector procurement, especially in the NHS. – Says he would “recycle roughly half” of the savings made by the spending review into frontline services, such as teachers and nurses.
– Pledges to invest more into education, especially for those in “mid-life”. – Vows to put a long-term plan in place to tackle the issue of social care in the UK. – Says people should not have to pay hospital car parking charges to visit a sick relative or wait four weeks for a GP appointment.
On Tuesday 18 June BBC One will host a live election debate between the Conservative MPs still in the race.
If you would like to ask the candidates a question live on air, use the form below. It should be open to all of them, not a specific politician.