* May likely to face criticism and anger
* Seen surviving as prime minister for now
* Seeks deal with Northern Ireland's DUP
* Brexit talks due to start on June 19
By Michael Holden and Kate Holton
LONDON, June 12 (Reuters) - Prime Minister Theresa May will try to convince lawmakers from her Conservative Party on Monday that she should remain as leader after a disastrous gamble on a snap election that weakened Britain's hand just days before formal Brexit talks.
May looked set to face criticism and anger from Conservative MPs at a private meeting in parliament over her handling of an election that lost the party its parliamentary majority.
The Conservatives won 318 seats out of the 650 in last Thursday's vote, meaning they now require support to govern and have chosen the eurosceptic Northern Irish Democratic Unionist Party (DUP), which has 10 seats, for that.
However, despite the shock result and speculation there could soon be a leadership election, May's position appeared safe for at least the immediate days ahead.
"I don't detect any great appetite amongst my colleagues for presenting the public with a massive additional dose of uncertainty by getting involved in a self-indulgent Conservative Party internal election campaign."," Graham Brady, chairman of the 1922 Committee of Conservative lawmakers, told BBC TV.
If she fails at the meeting to reassure lawmakers that she can govern effectively however her critics are likely to step up calls for her to go.
Senior figures, including Foreign Secretary Boris Johnson who is touted as the favourite to replace May should she be forced out, have pledged loyalty and called on colleagues to rally behind her.
In a further bid to win over disillusioned lawmakers, May appointed Michael Gove, a long-serving cabinet minister with whom she has clashed in the past, as environment minister while two of her closest aides, who many blamed for the election result, resigned.
However, George Osborne, a former finance minister who is now editor of London's Evening Standard newspaper and a vocal critic of May, said she appeared a "dead woman walking".
On Tuesday, May is due to meet the DUP leader Arlene Foster to finalise a deal to ensure support for May's minority government on major issues.
Brexit Secretary David Davis said that some policies planned before the election would be pruned back.
The political turmoil comes a week before Britain is due to start negotiating the terms of its exit from the European Union in talks of unprecedented complexity that are supposed to wrap up by the end of March 2019, when Britain actually leaves.
That timeline now looks even more ambitious than before, not least because May's electoral debacle has emboldened those within her own party who object to her "hard Brexit" approach of leaving the European single market and customs union.
"The interpretation that we have put on it ... is that people voted for three things in essence, control of borders, control of laws, control of money," Davis told BBC radio.
"In order to deliver that you can't do that inside the single market, so what do you do, you try and have the best possible access from outside."
Davis also said walking away without securing a deal with the remaining 27 EU states remained a possibility.
The uncertainty has hit business confidence, according to a survey by the Institute of Directors (IoD). It found a negative swing of 34 points in confidence in the UK economy from its last survey in May.
The pound slid to its lowest level for nearly two months after the vote, but the fall was much less severe than the one sparked by the Brexit vote in June 2016. On Monday, the currency was under pressure once again.
"It is hard to overstate what a dramatic impact the current political uncertainty is having on business leaders, and the consequences could – if not addressed immediately – be disastrous for the UK economy," Institute of Directors director general, Stephen Martin, said.
Additional reporting by Alistair Smout and James Davey; Editing by Guy Faulconbridge and Louise Ireland