UK Prime Minister Theresa May won a confidence vote in Parliament on Wednesday and then appealed to lawmakers to reach a consensus on Brexit.

"This evening the government has won the confidence of Parliament. This now gives us the opportunity to focus on finding a way forward on Brexit," May said outside 10 Downing Street in London.

"Now MPs have made clear what they don't want, we must all work constructively together to set out what parliament does want," she added.

Lawmakers voted 325 to 306 that they had confidence in May's government just a day after voting down her withdrawal agreement with the European Union. May now has until Monday to present her plan on how the government should move forward.

May said she believed Parliament had a duty "put self-interest aside" and deliver on the 2016 Brexit referendum result, in which UK citizens voted to withdraw from the EU.

"In a historic vote in 2016, the country decided to leave the EU," May said. "Now, over two-and-a-half years later, it’s time for us to come together, put the national interest first – and deliver on the referendum.

"I believe it is my duty to deliver on the British people’s instruction to leave the European Union and I intend to do so," she added.

Meeting with party leaders

After winning the no-confidence vote Wednesday, May held talks with party leaders to try to find a way forward on Brexit. 

The Conservative Party politician said she has already met with leaders of the Liberal Democrats, the Scottish National Party and the Welsh Plaid Cymru party. She intends to meet "senior government representatives" on Thursday, including members of Northern Irish coalition partner, the Democratic Unionist Party.

She also noted that Jeremy Corbyn, the leader of the opposition Labour Party who called for Wednesday's no-confidence vote, has yet to take her up on her invitation for further Brexit discussions. 

"I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open," May said. 

Corbyn said earlier Wednesday that no positive talks were possible unless a no-deal Brexit, a scenario in which the UK withdraws from the EU without a divorce agreement, was off the table. Many in his party want a permanent customs union with the European bloc, a close relationship with its single market and greater protections for workers and consumers.

Limited options left

The defeat of the EU withdrawal agreement in Parliament on Tuesday has left May with a narrow range of options regarding Brexit with 10 weeks until the UK's March 29 due date to leave the bloc.

Those options include:

• Proposing specific changes to the withdrawal agreement, which EU lawmakers have said is no longer negotiable

• Holding a second Brexit referendum, an option May has ruled out in the past

• Applying to extend to the March 29 deadline, which would allow the UK more time to put together a withdrawal agreement

• Leaving the European Union with no deal in place, which has been dubbed a "hard Brexit."

On Monday, May is expected to give a statement regarding the government's path forward regarding Brexit. If changes are made to the current withdrawal agreement, analysts believe the alterations will be minor and unlikely to sway skeptical MPs.