BORIS Johnson has formally launched his campaign for the Conservative crown by pledging to cut taxes, boost police numbers and increase spending on schools.

On Brexit, the former Foreign Secretary insisted under his premiership Britain would leave the EU “deal or no deal” on October 31.

Mr Johnson, still the bookies’ favourite to succeed Theresa May in Downing St, launched a campaign, which was clearly aimed at showing Tory MPs that he was the candidate most likely to secure them a general election victory with carefully chosen footage of the former Foreign Secretary on voters' doorsteps.

The launch came as senior colleagues urged some of the 13 candidates with little or no chance of succeeding in the “parliamentary Grand National” to pull out as the more candidates there were, the longer it could take to name a new leader.

The Prime Minister is set to relinquish her role as Tory leader on Friday; the leadership contest will then begin on Monday. But the first stage could last for weeks as MPs vote to eliminate candidates until two are left. These will then take part in nationwide hustings. It is widely thought that if Mr Johnson can get into the final two, he will win because of his support among the 120,000-strong membership.

The party’s plan is to name the new leader by the time Westminster rises for its summer recess in mid-July.

As well as extra funding for schools in England, Mr Johnson declared: “We need more police out there."

He suggested he could "cut some taxes and you get more money in" to pay for his campaign pledges.

Higher spending on schools would normally mean a knock-on windfall for the Scottish Government through the so-called Barnett Formula, by which Scotland per head gets a higher level of spending than England overall. However, Mr Johnson has been an opponent of this system, once describing it as “slightly reckless,” raising the possibility that if he became PM, he could seek to change the system and lessen the amount of money Scotland gets.

The former London Mayor went on: "If there is one message in that referendum of 2016, it is that too many people feel left behind, that they are not able to take part fully in the opportunities and success of our country. That's why now is the time to unite our society and unite our country.

"To build the infrastructure, to invest in education, to improve our environment and support our fantastic NHS.

"To lift everyone in our country and, of course, also to make sure that we support our wealth creators and the businesses that make that investment possible. Now is the time for us to believe in ourselves and what we can do," declared the London MP.

Meanwhile, Ken Clarke, the former Chancellor, was critical of the leadership contest, saying: "It is all a shambles and is in danger of becoming a rather tragic farce unless some order is brought into it. There is nothing I can do about that; the 1922[backbench] Committee perhaps should have tightened up the rules before we started."

The Europhile Tory is backing Rory Stewart, the International Development Secretary, who is against a no-deal outcome. Mr Clarke insisted the Scot had a “chance" of succeeding Mrs May as the next PM and "shake up the present establishment of the party".

"I have never seen the Conservative Party in such a crisis. I do think it is tearing itself apart. It is polarising into simplistic positions," he declared.

James Brokenshire, the Communities Secretary, urged some colleagues in their “scramble” for the leadership consider pulling out of the race to "speed things up," now they have "provoked some ideas and thoughts".

He suggested no-hopers were wasting everybody's time, saying there should only be "a small handful of candidates" in the running because "we just don't have the luxury of time".

His point was echoed by Chris Grayling, the Transport Secretary, who noted: “I hope those who are not really, numbers-wise, in the running, will think twice about whether they really want to go ahead with their candidacies.”

Elsewhere, Esther McVey, another Tory leadership hopeful, doubled-down on calls she made for parents to be able to decide if their children should learn about LGBT relationships.

Last week, the former Work and Pensions Secretary told Sky News: "Parents should have the final say on what they want their children to know."

Asked about these comments on the BBC's Victoria Derbyshire programme, Ms McVey said: "These were very young children in primary schools and I said the people who should know whether it is age-relevant are the parents not the state.

“Parents with very young children...four and five-year-olds and I would say that is a young child...their parents know for their child what is age-relevant.

"And by the way, this is not controversial. This is the same policy that Justine Greening oversaw. It is the same policy that Labour oversaw."

The Cheshire MP added: "For young children in this multicultural, diverse, modern society that we live in, I would say for very young children, as you say four and five, parents have the say over sex education. But I happily agree and I welcome that LGBT rights are taught within sex education."

Ms Greening, the former Education Secretary, criticised the comments made by Ms McVey last week.

In a tweet, the London MP said: "You can't pick & choose on human rights & equality. Children should understand a modern & diverse Britain they're growing up in. Matters for social mobility too - you can't be your best if you can't be yourself."