Former Prime Minister Sir John Major has said he believes David Cameron will succeed in reclaiming powers from the European Union before holding a referendum on the UK's membership.
Sir John said the political climate following the European elections would give Mr Cameron "allies" in any talks.
He suggested the free movement of people around Europe could be "qualified in some way".
But he warned that an exit from the EU would leave the UK isolated.
Mr Cameron has promised to hold a referendum on EU membership in 2017, if the Tories win the next general election, so people can decide if they are satisfied with the concessions his government will have negotiated in the meantime.
Rows over Europe dogged Sir John's Conservative government, which faced a confidence vote in the House of Commons in 1993 over its decision to sign the Maastricht Treaty.
But speaking to BBC Radio 4's Today programme, Sir John said Mr Cameron's position was not "remotely" like the situation he faced as prime minister.
On Mr Cameron's bid to win back powers ahead of a referendum, he said: "It can be done and I think this prime minister can do it".
UKIP, which wants the UK to withdraw from the EU, came top in the European elections in the UK, and Eurosceptic parties also made gains in other countries.
The results have led to calls for a rethink of the role of Brussels, while European Council President Herman Van Rompuy said the vote had "sent a strong message".
Sir John said the elections had made it "apparent" that reform was necessary.
He said: "I think that gives a great deal of power to the British determination to renegotiate, because they will have allies today, which in the 1990s they did not have".
And he said changes could be made to the fundamental freedoms of the union, including the movement of people, saying: "You can't have an absolute restriction but you can qualify it in some ways".
There are a "whole range of things quite apart from freedom of movement where positive reform can be made", he added, saying the principle of subsidiarity - that decisions should be taken at national level if possible - had been overlooked in recent years.
A "reaffirmation" of the UK's membership would remove the political "bitterness" that had built up on the issue, he said.
And he played down the threat to the Conservatives from UKIP, who he said were "good at exploiting grievances" but were "not frankly a very tolerant party". He said their appeal was not likely to continue for a very long time, but they were "an impediment for the moment".
Those arguing for a UK exit from the EU were wrong as it was in the country's economic self interest to stay in, he added.