Boris Johnson has vowed to prove critics of Brexit wrong, describing them as "doubters, doomsters and gloomsters", in his first speech outside Downing Street as Prime Minister.

He spoke outside Number 10 for the first time after first meeting the Queen at Buckingham Palace and accepting an invitation to form a new government.

Johnson also vowed to protect the union and the integrity of the UK, praising the "awesome foursome" of the four home nations, which he said were greater together than the sum of their parts.

The new Conservative leader was appointed to replace Theresa May as PM after she formally resigned at palace just minutes earlier.

Johnson has vowed to abide by the Brexit deadline of October 31 "come what may", with or without a deal with the EU.

First praising his predecessor, the new Prime Minister said: "I pay tribute to the fortitude and patience of my predecessor and her deep sense of public service.

"But in spite of all her efforts, it has become clear that there are pessimists at home and abroad who think, after three years of indecision, that this country has become a prisoner to the old arguments of 2016 and in this home of democracy we are incapable of honouring a democratic mandate.

"And so I am standing before you today, to tell you the British people, that those critics are wrong - the doubters, the doomsters, the gloomsters are going to get it wrong again."

Johnson said that he will succeed in delivering Brexit by the Halloween deadline "no ifs or buts".

He said: "The people who bet against Britain are going to lose their shirts because we are going to restore trust in our democracy and we are going to fulfil the repeated promises of Parliament to the people and come out of the EU on October 31 no ifs or buts.

"And we will do a new deal, a better deal that will maximise the opportunities of Brexit while allowing us to develop a new and exciting partnership with the rest of Europe based on free trade and mutual support.

"I have every confidence that in 99 days time we will have cracked it.

"But you know what? We aren't going to wait 99 days because the British people have had enough of waiting.

"The time has come to act, to take decisions to give strong leadership and to change this country for the better."

The PM added he was "convinced we can do a deal" to resolve the issue of the Irish border but he would prepare for a no-deal Brexit.

Johnson vowed to be Prime Minister who will govern the whole UK, saying: "It is time we unleashed the productive power, not just of London and the South East, but of every corner of England, Scotland, Wales and Northern Ireland.

"The awesome foursome that are incarnated in that red, white and blue flag."

But responding to the speech, First Minister Nicola Sturgeon tweeted: "Behind all the 'make Britain great again' type rhetoric, that speech was rambling, blame-shifting and, to put it mildly, somewhat divorced from reality."

On the way to his appointment with the Queen, Johnson's car was briefly impeded by climate change protesters blocking the road.

Before May's departure, she received the resignations of Chancellor Philip Hammond, David Gauke and Rory Stewart from their Cabinet roles.

Her effective deputy prime minister David Lidington also announced he was standing down from the government.

Hammond, Gauke and Stewart strongly oppose a no-deal Brexit and oppose Johnson's commitment to take Britain out of the EU by Halloween "do or die".

In her parting remarks from No 10, May warned her successor to seek a Brexit "that works for the whole United Kingdom".