Prime Minister Theresa May said: “This is an historic moment from which there can be no turning back – Britain is leaving the European Union – we’re going to make our own decisions and our own laws, we’re going to take control of the things that matter most to us.

“And we’re going to take this opportunity to build a stronger and fairer Britain that our children and grandchildren are proud to call home.”

Labour leader Jeremy Corbyn said his party respected the decision of the British people to leave the EU.

“Today we embark on the country’s most important negotiations in modern times.

“The next steps along this journey are the most crucial, and if the prime minister is to unite this country, as she says she aims to do, the government needs to listen, consult and represent the whole country, not just the hard-line Tory ideologues on her own benches.”

Scottish First Minister Nicola Sturgeon tweeted: “Today, the PM will take the UK over a cliff with no idea of the landing place. Scotland didn’t vote for it and our voice has been ignored.”

Lib Dem leader Tim Farron said: “I believe the prime minister is twisting the will of the people, leaping into the abyss without any idea of where our country will end up.

“Theresa May has chosen the hardest and most divisive form of Brexit, choosing to take us out of the single market before she has even tried to negotiate.”

European Council President Donald Tusk said invoking Article 50 was not a happy occasion. “There is nothing to win in this process – and I am talking about both sides. In essence, this is about damage control.

“We already miss you. Thank you and goodbye.”

Former UKIP leader Nigel Farage said he felt “thrilled because I know that at 12:30 today we passed the point of no return”.

He added: “There will be lots of arguments and debates over the next few years – but we’re leaving, so I couldn’t be happier really.

“I’ll go for a pint of something and think to myself that, after 25 years of slog, perhaps it was all worth it.”

Former Labour leader Ed Miliband urged Mrs May to work hard to recapture the national unity “which, frankly, eludes us at the moment”.

“The eventual deal we get must work for the 48% as well as the 52% because, whether we were Remainers or Leavers, we’ll all live in the same country together after Brexit.

“But can I emphasise to her that national unity must be earned and not just asserted, and it must be shown in deeds and not just in words? And we are a long, long way from it, and I hope that she’ll agree with that.”

SNP Westminster leader Angus Robertson said: “She said she thinks Brexit will bring unity to the United Kingdom. It will not. On this issue it is not ‘a United Kingdom’, and she needs to respect the differences across the nations of the UK. If she remains intransigent, she will make Scottish independence inevitable.”

Stephen Martin, the Institute of Directors director general, urged ministers to go for a smooth Brexit, with new trading arrangements agreed “before we walk through the exit door”.

“Success means listening to business on the vital priorities of maintaining tariff-free trade, minimising customs red-tape and keeping the bureaucratic hurdles to bringing in necessary skills as low as possible.”

Paul Drechsler, CBI president, said: “It is in the interests of businesses across Europe to work together in absolute determination to make a success of Brexit.

“Our shared aim must be to forge a mutually beneficial deal that delivers barrier-free trade and safeguards prosperity for all. The prime minister has recognised this.”

Former Conservative minister Alistair Burt said: “Like millions of others in the United Kingdom, I’m proud of the European Union and the contribution the United Kingdom has made to the European Union during my political lifetime, and I am a little sad today. But I do stand unequivocally with the prime minister as she calls for a united approach to a new future.”

European chief negotiator for Brexit Michel Barnier told the BBC he had read Theresa May’s letter to the EU, triggering Article 50, adding: “We’re ready.”

TUC general secretary Frances O’Grady urged the prime minister to take her time “to get the best deal for Britain – not just the fastest deal”, adding: “British workers and British jobs are relying on it.

“The best deal will guarantee that hardworking Brits keep their hard-won rights at work – and that in the years to come they won’t miss out on new protections that Dutch, Spanish and German workers get.”

Former Labour shadow home secretary Yvette Cooper said the prime minister must not “unintentionally lead the break-up of Britain” through her pursuit of Brexit.

“But she will also know that holding us together requires more than just the rhetoric of unity, so can she say what she will do in both the content and style of your negotiations?

“Not to fuel further division, not to play into the hands of others but to ensure that voices from all over the country are genuinely heard in this debate, so that she does not become the prime minister who unintentionally leads the break-up of Britain.”

Gina Miller, the businesswoman who brought the landmark legal challenge to get Parliament to vote on whether the UK could begin the process of leaving the EU, said she was “filled with trepidation and anxiety” following the triggering of Article 50.

“There seems to be very little understanding of the reality of what’s going to face us in these negotiations.

“It seems to be ‘Mrs May’s way or no way’ – that closed stance is not best for the whole of Britain”.

Former Conservative minister Claire Perry praised Mrs May’s “clear, concise and very generous” approach to the Brexit talks, but urged her to reject the idea that no deal would be OK.

“As we go into a period of really enhanced risk and uncertainty for our country and for businesses… does she not agree with me it’s time to start talking facts and sense to the British people rather than rhetoric and ideology?

“In particular, rejecting the idea that no deal and a reliance on WTO [World Trade Organisation] rules would somehow be OK.”

Former Conservative Education Secretary Nicky Morgan warned of the dangers of crashing out without an agreement – a move the prime minister has repeatedly said she is prepared to make if the EU does not give her a good deal.

“Could she say how she is going to keep Parliament fully engaged, this Parliament, throughout that process, and also that she will do her utmost to secure a trade deal that we can all support and she will not listen to the siren voices who seem to think that no deal is a good option.”

Plaid Cymru Westminster leader Hywel Williams told Mrs May: “There must be a better way than just her way.”

“Fairness is just that, the proper respect for all views from all parts of the island, not just, as she puts it, taking into account specific interests of nations and regions beforehand, not just consulting on which repatriated powers should stay in Westminster and which should be dribbled down, whilst she drives through her extreme version of Brexit.”

DUP deputy leader Nigel Dodds said his party believed Mrs May to be the right leader to steer the country through the Brexit challenges ahead.

“The prime minister has rightly been emphasising her determination to deliver for all constituent parts of the United Kingdom on this historic day.

“And whilst others are content to moan and whine, we want to see that delivery happen and we are confident she will make that happen.”

Former Conservative minister Anna Soubry urged the prime minister to reconsider staying in the single market if the EU abandoned its commitment to the free movement of people.

“It’s what British business wants, it would see off Nicola Sturgeon and the SNP’s outrageous demands for a second referendum, and these are serious matters that this United Kingdom faces.”

Miles Celic, chief executive of TheCityUK, called for continued access to high quality talent from Europe and beyond.

“For the UK-based financial and related professional services industry, the right Brexit deal will be bespoke, underpinned by mutual market access and based on mutual recognition and regulatory cooperation.”

Antonio Tajani, President of the European Parliament, said: “Today isn’t a good day. Brexit marks a new chapter in our union’s history, but we’re ready, we’ll move on, hoping the UK remains a close partner.”

Former Conservative Deputy Speaker Nigel Evans said: “Well this is truly a red, white and blue letter day, and it represents all of the constituent parts of the United Kingdom, including Scotland. Sending it ambassador class was a nice touch, prime minister.”

The SNP’s Owen Thompson said: “The prime minister told us Brexit meant Brexit.

“But now when we see the Scottish parliament voting for a second Scottish referendum, would the prime minister realise and acknowledge that Scotref means Scotref, and agree to any application for a Section 30 [the order allowing a second Scottish independence vote]?”