Britain's attempt to forge a new relationship with the European Union has officially started with positive words but little detail, and months of tough negotiations ahead. British Prime Minister David Cameron tweeted Friday that he had made "significant progress" at a meeting of EU leaders in Brussels. "It's been agreed a renegotiation of our membership of the EU can begin."Britain will hold a referendum on EU membership by the end of 2017, and Cameron wants major changes to the U.K.'s relationship with the 28-nation bloc as a condition of remaining in.At Thursday's meeting, EU leaders agreed to begin talks on Britain's wishes, though that was far from the summit's priority. PM Cameron spoke on the topic for only a few minutes during talks preoccupied with the Greek debt crisis and thousands of migrants attempting to cross the Mediterranean to Europe. EU President Donald Tusk said "we should consider British concerns, but only in a way that will be safe for all of Europe." "The fundamental values of the EU are not for sale and so are non-negotiable," he said.Civil servants will now draw up detailed plans for talks, and EU leaders will return to the issue in December. Estonian Prime Minister Taavi Roivas said Europe was open to Britain's ideas, and he hoped Cameron's renegotiation would succeed. "Because the EU is much better off with Britain inside ... Britain is better off while as a member of the EU," he told the BBC.PM Cameron will likely find allies on his bid to ensure protection for the nine EU countries, including Britain, that are not part of the euro single currency, and in efforts to win more powers for national parliaments to stop planned EU laws. But Britain's desire to tighten its grip on immigration will face strong opposition, since citizens' right to live and work in other member states is a fundamental EU principle. British Prime Minister Cameron, as part of the Conservative governments' legislative program, demanded structural changes in EU policies on immigration and border control. The proposed plan would reshape Britain's position in the EU, contingent upon the EU leaders' positive attitude toward EU reforms. The plan proposes "controlling migration by making it harder for EU migrants to claim state benefits in Britain, opting out of the EU's commitment to an 'ever closer union' and handing some powers back to national parliaments."Cameron said earlier that he will vote in favor of remaining in the EU if he can secure these changes, which include making it harder for EU migrants to claim state benefits in Britain. Opinion polls suggest so far that the majority of voters in Britain would back staying in Europe. A survey conducted by the Pew Research Center on the British mood over the EU exit shows that 55 percent of U.K. citizens are in favor of remaining part of the EU bloc. Thirty-six percent wants Britain to leave the EU bloc, the poll suggests. Compared to 2013 findings, this marks an increase, as only 46 percent of U.K. citizens favored EU membership in 2013 while 46 percent favored leaving.