The foundation for a "Global Britain", a bid for the "theft of democracy" or proof Theresa May wants "to have her cake and eat it".
The prime minister's plans for Brexit
Key figures in the rest of Europe have also had their say after watching her London keynote speech.
She has said leave the single market, but at the same time says she wants to have access to the single market. I'm not quite sure how that's going to go down in Europe.
Jeremy Corbyn, Labour leader 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. ... The people voted for departure, they should be given a vote on the destination. This is a theft of democracy.
Tim Farron, Liberal Democrat leader I already said it (a second Scottish independence referendum) was highly likely. The prime minister today, I think, has made it even more likely.
Nicola Sturgeon, SNP leader We're not leaving Europe, we're disentangling ourselves from the treaties of the EU.
Boris Johnson, Foreign Secretary Out of the single market, possibly out of the customs union, then investment in core sectors like car manufacturing, chemicals, aerospace, even food manufacturing, will be threatened as companies face hefty on-costs and serious disruption to their supply chains.
The Prime Minister must pay less heed to the Brexit headbangers around the Cabinet table and more to the anxiety felt by working people who believe their jobs are being held hostage by the extreme nationalist wing of her Government.
Len McCluskey, general secretary of Unite
Unite chief Len McCluskey said jobs will be threatened by the PM's chosen course of action. Credit: PA Working people are worried they will end up paying the price of leaving the single market. There is real concern that it will be bad for jobs, bad for rights at work and bad for the living standards of British people.
FRANCES O'GRADY, LEADER OF THE CONGRESS UNION We welcome the level of detail provided in the PM's speech and her commitment to providing certainty wherever possible.
Allie Renison, Institute of Directors
The Institute of Directors welcomed the 'level of detail' given by Theresa May. Credit: PA The Prime Minister has provided important clarity ahead of the triggering of Article 50 and the start of formal Brexit negotiations.
Paul Everitt, chief executive of aerospace and defence trade body ADS While businesses now have a clearer sense of the Prime Minister's top-line priorities, they will come away from her speech knowing little more about the likely outcome of the Brexit negotiations than they did yesterday.
Adam Marshall, director general of the British Chambers of Commerce Today’s announcement is the starting point for a 'pro-business Brexit. We now want to see concerted action to address trade, talent and transitional arrangements.
Mike Cherry, National Chairman at the Federation of Small Businesses Whatever position people take on Brexit, it's a fact that leaving the single market would undermine vital environmental and consumer protections we now take for granted.
Many of the laws that keep our bathing water clean and control dangerous air pollution and toxic chemicals come from the EU.
Without EU laws and courts to underpin and enforce them, they could be left at the mercy of ministers who may ignore them and scrap them with a stroke of the pen.
Rosie Rogers, Greenpeace UK's head of public affairs
The administration led by Taoiseach Enda Kenny has identified risks and opportunities in Brexit. Credit: PA She made clear that her priorities include maintaining the common travel area and avoiding a return to a hard border with Northern Ireland, both of which are welcome.
The (Irish) Government is under no illusion about the nature and scale of the Brexit challenge ... (and) acutely aware of the potential risks and challenges for the Irish economy.
The (Irish) Government is also very aware of the potential economic opportunities that may arise for Ireland, including in terms of mobile investment. Economic opportunities for Ireland will be pursued vigorously.
French right-wing presidential candidate Marine Le Pen Credit: AP I think she makes European Union leaders swallow their own sarcasm when they continuously said for months that she will come back with her pants down to try to obtain a kind of - soft Brexit - and she came to say - 'no, we are going to renegotiate the totality of treaties that link us to the EU'. So I consider that all of this corresponds to democracy.
French right-wing presidential candidate Marine Le Pen The German foreign minister said the speech had created "clarity".
We welcome that the British prime minister ... has finally created a little more clarity about the British plans. She has underlined that Great Britain is striving for a positive and constructive partnership, a friendship, with a strong EU. That is good.
We too want the best, closest and most trusting relationship and wish for constructive negotiations with this goal.
>
FRANK-WALTER STEINMEIER, GERMAN FOREIGN MINISTER European Council president Donald Tusk led reaction on Twitter.
Other significant European voices included the Czech secretary of state for EU affairs Tomas Prouza, Finnish finance minister Petteri Orpo and former Swedish foreign minister and prime minister Carl Bildt.
