Theresa May Brexit speech as it happened: PM warns European values will be crushed into tiny pieces if EU tries to punish Britain

ITV's Robert Peston is asking whether the PM was "wrong" about her previous words..

.. May says everyone knows she campaigned on the Remain side. But the Government is made up of both sides. 

.. on the final Brexit deal going to the Commons, May adds: "There will be a vote for the British Parliament". 

The speech is now over. Downing Street billed the speech to be significant - and it clearly was. Here is a quick summary.

1. Britain will leave the single market - but have some access to it, through a tariff-free trade deal. However, Philip Hammond, the Chancellor, beat her to it: 

2. May confirmed the Commons will have a final vote on any Brexit deal  - but she refused to say, when asked by ITV, what would happen if MPs voted against the Government 

3. She says Britain will not remain a full member of the customs union:

4. She threatened "no deal" with the EU if the nations attempt to punish Britain.

Caroline Lucas, the co-leader of the Green Party, has responded to Theresa May's speech on Brexit saying she is taking an "extreme gamble" with the UK's future: 

“Theresa May has confirmed today that she is willing to take an extreme gamble with our country’s future. Her plan for Britain to be out of the Single Market and out of the Customs Union, without any guarantees on the kind of bilateral trade deals we’ll have, is extremely risky. The Prime Minister has morphed a close-run referendum into a mandate for an extremely hard brexit which will see our economy harmed as part of her desperate desire to end free movement.

“Theresa May’s veiled threat to the EU about Britain setting its 'own economic model’ if we don’t get a good deal is deeply concerning because, in effect, she means turning Britain into a corporate tax haven floating on the edge of Europe. The Green Party will continue to stand up for free movement and keeping close ties with the European Union, and we’ll fight any attempt to slash our state through corporate tax cuts and a race to the bottom on regulations.” 

Liberal Democrat leader Tim Farron responds to May's speech:

“Theresa May has confirmed Britain is heading for a Hard Brexit. She claimed people voted to Leave the Single Market. They didn’t. She has made the choice to do massive damage to the British economy.

“Theresa May also made clear that she will deny the people a vote on the final deal. So instead of a democratic decision by the people in the country, she wants a stitch-up by politicians in Westminster. The people voted for departure, they should be given a vote on the destination. This is a theft of democracy.

“This speech was a mixture of vague fantasies and toothless threats to our nearest neighbours. At the moment Britain needs friends more than ever, she has succeeded in uniting the rest of Europe against her.

“When it comes to British prosperity and British democracy, she is waiving the white flag from the White Cliffs of Dover.

"Only the Liberal Democrats are fighting to keep Britain open, tolerant and united, and are the real opposition to the Conservative Brexit government."

Foreign Secretary Boris Johnson said Mrs May's "powerful" speech will be "well received" by EU nations.

Speaking to reporters at Lancaster House, he went on: "Because it's negotiable, this is something that I think will be good for the UK and good for the rest of the EU as well."

Asked why the EU would give the UK a "free lunch", Mr Johnson said: "As the Prime Minister said, I think it's going to be good for both sides."

He went on: "We very strongly think this is in our mutual interest. We're not leaving Europe, we're disentangling ourselves from the treaties of the EU. We can remain powerfully committed to Europe with a new European partnership ... whilst also going forward with an identity as Global Britain."

This is from the Press Association

European politicians seemed largely unimpressed with the content of Theresa May's first major Brexit speech, in which the Prime Minister announced the UK would leave the single market.

MEPs from across the continent took to Twitter as the speech unfolded, with one German MEP accusing the PM of "bluntly making fun of her electorate".

Jan Philipp Albrecht, a Green MEP for northern Germany, tweeted: "May: Go f*** yourself EU but please don't let us down. *whine* *whine*"

This is from the Guardian's political editor Heather Stewart: