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Cameron's 'given in to hardliners'
David Cameron appears to have conceded "game, set and match to the hardliners in his party", former Labour Cabinet minister Lord Mandelson said.
Lord Mandelson, who also served as a European commissioner, said of the Prime Minister's speech: "It is not a search together in unity with our partners in Europe.
"Effectively, it's an ultimatum to them with a deadline, with the Prime Minister not saying he will get the best deal for Britain and then recommend that we stay in because that's in our national interest to do so, he is actually leaving open the option to recommend against the deal he gets and to Britain leaving the European Union altogether," he told BBC Radio 4's Today programme.
"That's quite a major step for a British prime minister to signal."
He said there was a "huge overlap of thinking between Britain and other member states" over measures to push growth, to make institutions more accountable and reduce regulation and business costs.
"In my view, what he is doing is treating the European Union like a cafeteria service at which you arrive with your own tray and try to leave with what you want.
"Whether you believe that Mr Cameron's European gamble is a sincere attempt to reform and improve the European Union or a cynical ploy to head off opposition to his leadership in his own party, there is no mistaking he is playing for very high stakes indeed and I do not believe he is going to get what he wants by attempting to put a pistol to the heads of his fellow member states."
He said Labour leader Ed Miliband faced "a difficult call" but he had been clear in his views.
Pro-Europeans had failed to do enough to inform the public of the benefits of membership over the years, he conceded, because they had "won the argument without making the case".
Ukip leader Nigel Farage said the referendum promise was a vindication of his party's long struggle but warned that securing a no vote would be tough and Ukip's "real job starts today".
He questioned whether the Prime Minister was serious about repatriating powers or simply looking to win back eurosceptic voters to the Tories.
"Winning this referendum, if and when it comes, is not going to be an easy thing but I feel that Ukip's real job starts today," he told Today.
"For the first time, a British prime minister is at least discussing the fact that leaving is an option.
"I remember many long, very lonely years in Ukip when, without a friend in the world, we were advocating this point of view.
"What today means is that in terms of the overall debate, the genie is out of the bottle and from now on the European debate will be taking place on terms that Ukip wants."
He went on: "If Mr Cameron was really serious about renegotiation, then he would invoke Article 50 of the Lisbon Treaty, which is the only mechanism that exists within the treaties to take powers back.
"If he did that ... I will take him seriously, but really I think all he is trying to do is to kick the can down the road and get Ukip off his back."
Shadow business secretary Chuka Umunna said the referendum promise would mean "five years of uncertainty" that would harm investment in the UK.
"After this speech today we know that global companies looking to situate European headquarters are probably going to shy away from the UK, which will cost growth and cost jobs," he said.
He declined to rule out Labour matching the referendum promise, saying only that the party supported existing legislation guaranteeing a public vote on any transfer of powers to Brussels.
"We have been very clear about our position and you have to act responsibly in the national interest," he said.
"This is certainly not a choice between reform and exit. It is an issue of whether or not you want to stay in and change the European Union in the national interest or whether you just walk away."
Former Lib Dem leader Paddy Ashdown said: "Mr Cameron has effectively told us that it is his intention to put Britain on a one-way street to leaving Europe."
Richard Ashworth, leader of the Conservative MEPs, urged the party to "get behind this vision, to support the PM's strategy and to meet the challenge of helping the EU become a more flexible and friendly place for Britain".
He added: "Too many European people today see European union as the cause of our problems, not the solution to those problems. That is why they have lost confidence in the Union. If we are to restore that confidence, that means change.
"Europe successfully confronted many of the problems that were facing our parents' generation. Now it's our turn to build a different kind of Europe, a Europe fit for our children's' generation."
Tory MP Dominic Raab hailed a "moderate, statesman-like approach ... rightly focused on a fundamental change in strategic direction rather than tactics".
"The ball is now in the EU's court," he said.
Dozens of colleagues flooded Twitter with positive reactions to the speech
Andrea Leadsom - one of the founders of the backbench Fresh Start group which has published a manifesto for powers to be returned from Brussels - said the speech was "spot on".
She said it was unlikely the renegotiation would not result in changes to the relationship.
Senior eurosceptic Bernard Jenkin told the BBC it was "a very, very big moment" for British politics and said he would vote to exit the EU if there was no "fundamentally new relationship".
Former Liberal Democrat leader Sir Menzies Campbell said: "This is more about Ukip than it is about the UK.
"The Prime Minister's efforts to reconcile his own position with that of his eurosceptic backbenchers leads logically to the position that if he could not get what he wanted out of Europe, he would be willing for the UK to leave.
"This will hardly commend his approach to those in the EU whose co-operation he requires."
CBI director general John Cridland said: "The EU single market is fundamental to Britain's future economic success, but the closer union of the eurozone is not for us.
"The Prime Minister rightly recognises the benefits of retaining membership of what must be a reformed EU and the CBI will work closely with Government to get the best deal for Britain."
Alyn Smith, a Scottish National Party MEP, said the Tories are the "true separatists".
The only way for Scotland to guarantee a "valued" position in the EU is by voting Yes in the Scottish independence referendum in autumn next year, he said.
"This wasn't a speech made to defend Scotland's or the UK's position in Europe. It was aimed purely at appeasing the fantasyland Europhobes who now make up a depressingly large and growing part of the Conservative Party," he said.
"In reality, the Prime Minister is offering a choice which he can never deliver, as the other members of the EU won't wear it. If you join a club, you can't then single-handedly rewrite the rule book and expect everyone else to accept it. In that sense, Emperor Cameron has no clothes."
He conceded that the EU needs reform but added: "The critical thing here is that David Cameron and the Tories cannot and do not speak for Scotland or for Scotland's interests. As part of the UK, we don't do as well as we should in Europe and we are incapable of making a full contribution.
"Never has it been clearer that Scotland needs independence. Our interests lie firmly at the heart of Europe, and it is becoming more obvious by the day that it is the Tories who are the true separatists.
"There is now only one way for Scotland to guarantee its future as a valued member of the European Union - by voting Yes in next year's referendum on independence."
He added: "Sad though I am to say it to our English neighbours, the core message they should take on board is: Be Very Afraid."
London Mayor Boris Johnson said: "David Cameron is bang on. What most sensible people want is to belong to the single market but to lop off the irritating excrescences of the European Union.
"We now have a chance to get a great new deal for Britain - that will put the UK at the heart of European trade but that will also allow us to think globally.
"The future of London is to remain the financial and commercial capital of Europe, to have a unique relationship with America - and to build our growing position as the capital of the BRICs and other emerging economies.
"That is a deal that would be in the interests of Britain and of Europe. If it is put to us in a referendum, I have no doubt that the British people would vote for it.
"The British people have not been consulted since 1975, and it is high time that they were. As the date for that referendum draws closer, it will be ever clearer that Ed Miliband has made a fatal goof in ruling it out."
Tory donor Lord Ashcroft said polling showed that Europe was not a major priority for voters.
In an article for ConservativeHome.com: "Tories must remember that we can only get what we want once we win an election. The more we talk about changing our relationship with Europe, the less likely it is to happen."
He added: "The new policy will be in the manifesto. The only question is whether we will get a chance to implement it - and that depends on whether we get a majority at the next election. And that depends on how voters think we are doing on the economy, jobs, public services, welfare, crime, immigration: whether we are on their side and understand their priorities.
"It is time for Tory Eurosceptics to declare victory and talk about something else."
Fiona Hall, leader of the Liberal Democrat delegation in the European Parliament, said: "Today David Cameron spoke not as Prime Minister but as a Tory Party leader backed into a corner by his outspoken tea-party backbenchers.
"He promised an in-out referendum on an uncertain renegotiation of the UK's relationship with the EU that leaves more questions than answers and creates a climate of uncertainty for investors.
"Instead of focusing all efforts on getting the British economy back on track, the Conservative Party will now be tied up in its own internal renegotiation discussions that have very little to do with the reality of treaty change among 27 member states.
"Cameron has failed to reassure our European partners over the UK's commitment to push for EU-wide reform rather than unilateral repatriation and cherry-picking.
"As a result, the UK will lose further influence in Europe as other member states anticipate a 'Brexit' and discount the UK's views altogether."