British Prime Minister David Cameron laid down a marker for Brussels, insisting British voters will not accept a "rigid" EU and that the UK's demands for reform must be heeded.
He said the EU "would not work" if it could not show "flexibility".
Mr Cameron was speaking after formally launching his bid to renegotiate the UK's membership ahead of the in/out membership promised by 2017.
He also said Greece would be likely to leave the euro if it rejects its bailout terms in a referendum.
Speaking on BBC Radio 4's 'Today' programme, Mr Cameron said Britain's interests would be best served by an agreement between the Greek government and the eurozone.
"If they vote no, I find it hard to see how that's consistent with staying in the euro because there would be a very significant default and a very significant problem," he said.
Mr Cameron said the EU had to be flexible enough to work for countries inside and outside the eurozone.
"If it can't show that flexibility it won't work as an organisation and I believe the British people will see that," he said, adding: "This needs to have the flexibility of a network, not the rigidity of a bloc."
Asked about raising his demands for reform during a summit dominated by the Greek and Mediterranean crises, Mr Cameron said there had been "very long" discussions about those two issues.
"In the middle of that there was a brief discussion about the British situation," which "got a very good reception", he said.
He said that there were many negotiations to come - "but every journey starts with a single step, as they say".
Meanwhile, Mr Cameron pledged a wide response to extremism, describing Britain as being united in grief over the beach massacre in Tunisia.