After bloodletting, UK's Eurosceptic party says united to push for EU exit

* Outcome triggered post-election turmoil, bloodletting

* Leader Farage says party now united again

By Andrew Osborn

LONDON, May 20 (Reuters) - The leader of the UK Independence Party said on Wednesday it was united and ready to campaign for Britain to leave the European Union as he tried to draw a line under a period of post-election turmoil.

UKIP, led by Nigel Farage, surged into third place with almost 4 million votes in a May 7 national election. But under Britain's winner-takes-all electoral system, it emerged with just a single place in the 650-seat House of Commons.

Bruised by the outcome, the party fell into a post-election power struggle with its campaign chief accusing advisers of creating a "personality cult" around Farage and a big donor calling on Farage to resign.

Farage did briefly quit, for three days, before saying he had been persuaded to stay on. Two of his aides later left the party, the campaign chief who'd spoken out resigned as economics spokesman, and the head of policy, who had said Farage needed to take a break, said her contract was coming to an end.

The turmoil made national headlines, in large part because Prime Minister David Cameron has promised to hold an in-out EU membership referendum by the end of 2017 and UKIP is one of the loudest voices campaigning for a 'Brexit' or British EU exit.

"What has happened in UKIP is since the election after the pressure cooker atmosphere of a campaign office one or two regrettable things were said and done by a very small number of people," Farage told BBC radio on Wednesday.

"I'll tell you where this leaves UKIP going into this referendum campaign unlike the other parties - united. 100 percent united."

In a show of unity, Suzanne Evans, the party's soon-to-be former policy chief, said separately she would remain deputy party chairman and loyal to Farage. She told the BBC it was "a coincidence" that she and others who had urged Farage to take a break had since seen their roles reduced.

Farage, a member of the European Parliament, said he suspected the EU referendum would be held in May 2016 to coincide with regional UK elections.

"We have a referendum on our hands," said Farage.

"I left the world of business to come into politics because I want Britain to have a trade relationship with Europe but not to be part of political union. So now is the time and that's why I've stayed in position." (Editing by Andrew Heavens)