UPDATE 1-"Let's come together," May makes Brexit appeal to party

(Adds May comments)

BIRMINGHAM, England, Sept 30 (Reuters) - Prime Minister Theresa May called on her party on Sunday to unite behind her plan to leave the European Union, making a direct appeal to critics by saying their desire for a free trade deal was at the heart of her own Brexit proposals.

At the start of what is set to be one of the Conservative Party's stormiest annual conferences, May's plans were once again attacked by two former ministers, with former foreign secretary, Boris Johnson, calling them "deranged."

Just six months before Britain is due to leave the EU in the country's biggest shift in foreign and trade policy in more than 40 years, the debate over how to leave the bloc is still raging in the center-right Conservative Party, and even in the government.

May's already fragile leadership was put under further pressure this month when the EU rejected parts of the so-called Chequers plan. But she put a positive spin on those talks, saying she was ready to consider to the EU's concerns.

"My message to my party is let's come together and get the best deal for Britain," May told the BBC in the central English city of Birmingham.

"At the heart of the Chequers plan is a free trade deal, a free trade area and frictionless trade ... Chequers at the moment is the only plan on the table that delivers on the Brexit vote ... and also delivers for the people of Northern Ireland."

May has shown little sign of shifting away from her Chequers plan, named after her country residence where she hashed out an agreement on Brexit with her ministers in July, despite growing criticism that her proposals offer the worst of all worlds.

Johnson, who quit May's cabinet after Chequers was agreed, called her plans "deranged" and attacked the prime minister for not believing in Brexit.

"Unlike the prime minister I campaigned for Brexit," Johnson, the bookmakers' favorite to succeed May, told the Sunday Times newspaper.

"Unlike the prime minister I fought for this, I believe in it, I think it's the right thing for our country and I think that what is happening now is, alas, not what people were promised in 2016."

Davis, who like Johnson resigned in protest said her plan was "just wrong," but he also said he thought it was 80-90 percent likely that the government would strike an exit deal with the EU.

TESTY CONFERENCE

May's team hoped the party's conference would give her a platform to renew her pledge to help those people who are "just about managing," trying to pull the focus away from Brexit and on to a domestic agenda.

But her first announcement - for an additional levy on foreign home buyers - did little to reset the conversation, with Sunday dominated again with Brexit, a possible leadership campaign and the prospect of an early election.

Johnson's interview in the Sunday Times was seen by many in the party to be the start of a campaign to unseat May - something that angered some Conservatives who are critical of the former foreign minister.

May refused to be drawn on his comments, and did not refer to him by name in a lengthy interview with the BBC. But her response was sharp.

"I do believe in Brexit," she said.

"But crucially I believe in delivering Brexit in a way that respects the vote and delivers on the vote of the British people while also protecting our union, protecting jobs and ensuring that we make a success of Brexit for the future."

And she did find some support.

Ruth Davidson, leader of the Scottish Conservatives, said she still believed May could still manage to win a deal with the EU, and her party chairman, Brandon Lewis, said he believed she could lead into the next election, due in 2022.

Davidson told Sky News that the EU summit in Salzburg had actually "slightly cleared the air actually, we know that officials are working very closely together."

"I think there is still a basis there for a deal to be done." (Writing by Elizabeth Piper Editing by Keith Weir)