* Summit sets negotiating terms for talks in June
* Row over UK budget veto shows potential acrimony
* Leaders say some Britons unrealistic on trade deal (Adds comments from UK Brexit minister)
By Alastair Macdonald and Philip Blenkinsop
BRUSSELS, April 29 (Reuters) - European Union leaders endorsed stiff divorce terms for Britain on Saturday and warned Britons to have "no illusions" about swiftly securing a new relationship to keep their access to EU markets.
At a Brussels summit marked by unusual harmony among the 27 leaders, there was a flash of the cross-Channel acrimony which some fear could wreck any deal when officials accused London of cynically vetoing some EU spending and demanded it back down or face disrupting the start of talks next month.
Meeting for the first time since Prime Minister Theresa May triggered the two-year countdown to Brexit in late March, her counterparts took just minutes as they sat down to lunch in Brussels to approve eight pages of negotiating guidelines hammered out by their diplomats over the past month.
They greeted the decision with applause, officials said.
The text will bind Michel Barnier, their chief negotiator, to seek a deal that secures the rights of 3 million EU expats living in Britain, ensures London pays tens of billions of euros Brussels thinks it will be owed, and avoids destabilising peace by creating a hard EU-UK border across the island of Ireland.
"We are ready," Barnier said. "We are together."
With Barnier expecting to launch negotiations after the June 8 election May called to strengthen her position, the EU leaders also firmly ruled out discussing the free trade deal May wants until they see "significant progress" on key withdrawal terms.
"Before discussing the future, we have to sort out our past," summit chair Donald Tusk told reporters.
He criticised British politicians -- who have included May herself -- for speaking of a quick deal to reassure expatriates when the legal complexities required much more detailed talks.
"We need a serious British response," Tusk said.
In London, Britain's minister for leaving the European Union said he wanted the negotiations to be conducted in a "spirit of goodwill".
"But there is no doubt that these negotiations are the most complex the UK has faced in our lifetimes. They will be tough and, at times, even confrontational," David Davis said in a statement in response to the guidelines.
German Chancellor Angela Merkel repeated her concern that some in Britain had "illusions" about quick trade talks.
"I sometimes feel some people in Britain, and I don't mean the government, are not so clear on the idea that there is an exit phase and then a phase on the future relationship," she said.
BRITISH "UNDERESTIMATE" DIFFICULTIES
European Commission President Jean-Claude Juncker, the EU chief executive, took an even more combative tone, saying his officials had identified a "cocktail" of 25 different legal issues to settle just regarding expatriate residence rights.
"I have the impression sometimes that our British friends -- not all of them -- underestimate the technical difficulties we have to face," he told reporters, three days after he and Barnier met May over dinner in London for "constructive" talks.
Raising publicly the Commission's irritation with Britain over its 11th-hour decision to withhold consent on Wednesday to some 6 billion euros ($6.5 billion) in EU spending on approved programmes, notably to handle the Mediterranean migrant crisis, Juncker warned that the issue could affect the start of talks.
British officials said the "reserve" imposed via a Tuesday night email on a package of measures due to have been approved by EU ambassadors on Wednesday morning was a simple procedural matter prompted by the "purdah" period before elections, during which ministers prefer not to take "sensitive" decisions.
Juncker was unimpressed: "It would facilitate the beginning of the negotiations if the UK were to be able to withdraw the reserve," he said.
EU officials questioned British motives, saying it appeared unprecedented and affected policies which Britain had agreed during months of prior deliberation: "This is clearly not a technical decision," one said. "It could be show of force."
An unusual unity has been forged by the shock of Brexit which broke a taboo and raised fears of further break-up at the hands of nationalists like far-right leader Marine Le Pen. She will contest France's presidential election run-off on May 7, though few expect her to beat centrist Emmanuel Macron.
The EU considers it vital that Britain not be seen to profit from Brexit, to dissuade others from following suit.
Belgian Prime Minister Charles Michel warned against falling into a "trap" where Britain divided the bloc to its advantage.
Also contentious among the 27 will be which cities scoop the prizes of hosting two EU agencies set to be moved from London.
With most of the 27 offering to house the European Medicines Agency (EMA) and several wanting the European Banking Authority (EBA), Tusk and Juncker proposed they agree selection criteria in June to avoid unseemly rows.
In a mark of how last year's Brexit vote has called into question the unity of the United Kingdom itself, leaders also offered Irish Prime Minister Enda Kenny a pledge that if Northern Ireland, which voted against Brexit, ever unites with his country, it will automatically be in the EU.
(Reporting by Philip Blenkinsop, Foo Yun Chee, Alastair Macdonald, Farah Salhi, Andreas Rinke, Jan Strupczewski and Alistair Smout; Writing by Alastair Macdonald; Editing by Janet Lawrence and Robin Pomeroy)