Below is an explanation of how May could face a leadership challenge under the ruling Conservative Party's rules:

- What needs to happen for there to be a leadership contest?

A leadership challenge can be triggered if 15 percent of the Conservative members of parliament (MPs) write letters demanding a confidence vote to the chairman of the party's "1922 Committee", which represents lawmakers who have no government jobs.

The Conservatives have 315 MPs so 48 would need to write such letters for a confidence vote to be called.

- Could this happen to May?

Some eurosceptic MPs say publicly they have submitted such letters in protest over her Brexit negotiating strategy. However, the 1922 Committee chairman Graham Brady is the only person who knows how many have done so, including those who have written to him confidentially.

Brady was reported as saying this month that some MPs have claimed to have submitted letters, when if fact they had not.

- What will happen during a confidence vote?

All Conservative MPs could vote for or against their leader. If May wins she remains in office and cannot be challenged again for 12 months. If she loses, she must resign and is barred from standing in the leadership election that follows.

- How quickly can a no confidence vote take place?

Under Conservative rules, the 1922 Committee chairman in consultation with the party leader decides the date of a vote, to be held as soon as possible.

In the last no confidence vote against a Conservative leader in 2003 - when the party was in opposition - it was held the day after the 1922 Committee chairman announced he had received enough letters to trigger the vote.

- What would happen if May lost a confidence vote?

If May lost a confidence vote there would be a leadership contest to decide her replacement. However, a general election would not automatically be triggered, and her replacement would become prime minister.

If several candidates come forward, a secret vote is held among Conservative MPs to whittle down the field. The candidate with the fewest votes is removed and another ballot among Conservative lawmakers is held. The process is repeated until two candidates remain, with votes held several days apart on Tuesdays and Thursdays.

The final two candidates are then put to a postal ballot of the wider Conservative Party membership, with the winner named the new leader. Voters need to have been party members for more than three months.

When David Cameron decided to step down as prime minister and Conservative leader after the EU referendum in 2016, five candidates came forward. The field was narrowed to May and then-junior minister Andrea Leadsom but she pulled out before members voted, leaving May to become leader unopposed.

- Who could replace May?

The list of possible replacements is long, but there is no clear frontrunner. Many of those expected to run used the Conservative Party's annual conference this month to set out their platform and priorities for any leadership bid.