* Britain faces worst political instability for decades

* Premier lost majority in ill-judged election

* Moves to oust May on hold to let her get started with Brexit

* May given time to carry out pledge to clean up post-poll "mess"

By Elizabeth Piper

LONDON, July 5 (Reuters) - It's lonely at the top for British Prime Minister Theresa May but she's holding on -- for now.

May faced calls to quit from inside and outside her ruling Conservative Party after losing its parliamentary majority in an ill-judged election that she did not need to call, plunging Britain into the worst political instability for decades.

She has struggled since then to unite her government on policy and to assemble a new team of aides -- one Conservative lawmaker described it as "career suicide" to agree to serve a leader whose days in office may be numbered.

But party sources say moves to oust May are now on hold after senior figures agreed she should be the one to at least make a start on two years of Brexit talks that are likely to stretch her government and possibly the public's patience, giving the world's fifth biggest economy some breathing space.

If she fails to make headway or satisfy some of her more eurosceptic party members, then she can answer for it, the party sources said.

"She'll stay for as long as we want her to," one lawmaker told Reuters, on condition of anonymity. "Now is not that time."

Concerns over the reaction of Britons if asked to vote for the fourth time in just over two years, over losing Conservative seats and of having someone else take over the lead in talks with the European Union have calmed calls to replace May.

Even the most embittered lawmakers say a new leadership vote would simply deepen divisions in the party over Brexit and its austerity agenda, blamed by opposition politicians for a devastating fire in west London that killed at least 80 people and for straining a police service battling militant attacks.

May, 60, has said she will carry on, despite her pride being "shattered" by the election, said one veteran Conservative Party member who spoke on condition of anonymity.

"But I suspect her sense of duty is bigger than (predecessor David) Cameron's," the source said. "No one actually wants the job, well they do want the job but not now."

CLEARING UP THE "MESS"

May, Britain's longest serving interior minister in over a century with a reputation as a tough and diligent politician, became the country's second female premier after Margaret Thatcher when Cameron resigned after Britons voted for Brexit.

Her path then was cleared when two other hopefuls -- her now foreign minister Boris Johnson and environment minister Michael Gove - all but killed off each others' bids and she appealed to members with her straight-talking can-do attitude.