European leaders lost no time on Friday in offering David Cameron talks on EU reform, bidding to ease uncertainty about Britain's future in the bloc ahead of the in-or-out referendum the prime minister will call now he has been re-elected.
France's Socialist president Francois Hollande invited the triumphant Conservative to Paris once he has formed a government in which, confounding opinion polls, he will no longer have to rely on coalition partners like the arch-europhile Liberal Democrats.
Jean-Claude Juncker, the EU's new chief executive whose team is already working to cut the kind of red tape and interference that angers many Britons, sees scope for reform short of major treaty changes and told Cameron: "I stand ready to work with you to strike a fair deal for the United Kingdom in the EU."
Hollande, German Chancellor Angela Merkel and leaders of the EU institutions in Brussels should offer a variety of fixes for gripes the generally pro-Europe leader of an often eurosceptical party says must be sorted out before he puts British membership to an unpredictable popular vote within a couple of years.
But the EU executive again stressed that there could be no renegotiation of basic treaties that irk Britons opposed to immigration from poorer EU states. In any case, as Hollande will surely tell Cameron, governments like Paris, which need referendums to ratify treaties, are in no position to get such measures past their own increasingly europhobic electorates.
European Commission President Juncker is also ready for talks and said he looked forward to hearing concrete proposals from Cameron, who has listed a number of general demands since promising the plebiscite in early 2013 to appease Conservative eurosceptics and outflank the rising UK Independence Party.
After two years of saying little and quietly hoping the issue might go away if Cameron lost power, EU leaders woke up on Friday realising they now must confront the problem head on.
For all the exasperation with Britain's love-hate relationship with the continent, most think the Union would be weakened by the loss of its second biggest economy, a global commercial power with significant military and diplomatic clout.
Paris and Berlin are ready to study British demands for EU reform "if that allowed them to argue for staying in the EU", a French government source told Reuters.
Stefani Weiss at German think-tank the Bertelsmann Stiftung in Brussels said other leaders had been unwilling to engage with Cameron while he was still only campaigning for re-election.
"This changes now. The Germans will be very forthcoming," she said, but warned that migration control was off-limits for nearly all other EU leaders. "There is a clear camp which wants to keep the UK, but also not at any price."
Those hoping for least disruption in the EU hope Cameron can use the surprising scale of his personal victory to sell a modest package of measures, some already in hand, to voters who recent polls suggest are more minded to stay in the EU.
While some Conservatives may demand more than the bloc is willing to concede in the way of sovereignty, Cameron may be able to curb any appetite for Brexit by using the threat of nationalist Scots breaking with London should it quit the EU.
Donald Tusk, the former Polish premier who chairs EU summits, praised Britain's "common sense" contribution to the Union and made a personal appeal to Cameron not to give in to compatriots who feel stifled by EU regulation.
"The United Kingdom plays a key role in ensuring that Europe has a common sense agenda, keeping the emphasis on a competitive economy through an effective single market, non-intrusive regulation, openness to trade with other nations, and a confident foreign policy," he said. "Objectives which I share."
Tusk, as president of the European Council which groups the 28 national leaders, will have a crucial role in forging any consensus on changing rules. An EU official said he would be keen to avoid a 27-against-1 row that could destabilise the EU.
Rather Tusk will try to generate a "positive debate" around making the bloc more efficient and more business-friendly.
Though some federalist voices, including former French premier Michel Rocard, have said so-called "Brexit" would remove a barrier to the "ever closer union" to which London is firmly opposed, many in France see Britain as a valuable counterweight to Germany, now Europe's clear economic and political leader.
Like Tusk, Juncker will play a key role along with Merkel and Hollande, both of whom have ruled out treaty change.
Despite Cameron's failed single-handed bid to stop Juncker's appointment last year -- alleging the Luxembourger wanted an EU super-state -- EU officials say the Commission chief is determined to forge a compromise.
Cameron's business allies want Britain to stay in the EU but the prime minister also needs something to show voters he has secured concessions, notably on being able to curb welfare benefits for migrants from poorer EU states, restoring powers to national parliaments and protecting London's financial market interests from being locked out of a more integrated euro zone.
With a first major debate likely at an EU summit in Brussels on June 25, Carl Bildt, the former Swedish prime minister, told Reuters said both sides would have to work fast to get any deal in place before Cameron must go to the country by 2017.
"Brussels will have to be open minded and listen to Cameron. Some substantive accord is needed and Tusk is the key person here. Berlin will also be very important," he said.
"Cameron now needs to reengage with Europe. He needs to come across with reform proposals that are achievable."
Charles Grant, director of the Centre for European Reform in London, said Cameron could highlight the programme of cutting bureaucracy and interference as well as plans to improve free trade inside the bloc that is already under way under Juncker.
"They'll have to dress that up to claim it's a British achievement," he said. "But it's happening already."
Mark Leonard of the European Council on Foreign Relations in London said Cameron had spoken of a need to change treaties but would have to accept the best he might get could be pledges to make amendments later when broader changes may be taking place.
"A lot of what he wants can be done with protocols and secondary legislation," Leonard said, noting Juncker's offers to stop short only of "major treaty change".
Michael Emerson, a long-time EU official and diplomat now at the Centre for European Policy Studies in Brussels, said the EU could, for example, offer some minor new regulations to make clear people cannot migrate across the bloc simply to claim benefits -- a view already supported last year by EU courts.
And Emerson believed Cameron, whose business allies are keen not to be excluded from the EU, could use fear of losing pro-EU Scotland to keep his eurosceptics in check to win a referendum in which recent polling suggests a majority prefer to stay in:
"Whereas the English Tories may be baying for blood," he said, "The Scottish factor will restrain him rather as the LibDems did in the last parliament."