British Prime Minister Theresa May departs from 10 Downing Street ahead of Prime Ministers Questions session (PMQs) in Parliament, London on May 22, 2019.

Theresa May resigned as Conservative Party leader on Friday, marking an end to a tumultuous three years at the head of U.K. politics. She will remain in her prime ministerial post only until a replacement is elected and the failure to deliver Brexit is already being scripted as her legacy.

Members of Parliament (MPs) voted down her proposed "withdrawal agreement" for a third time at the end of March, but May's departure may not necessarily mean that her blueprint for pulling the U.K. out of Europe will be completely discarded.

The withdrawal agreement — a 585-page document that outlines how the U.K. will leave the EU in March — is causing division among society and lawmakers.

"The withdrawal agreement is not Theresa's personal property, it stays in place" said Brexit Programme Director at the Institute for Government, Jill Rutter in a phone call to CNBC Wednesday.

"The EU didn't regard itself as negotiating with the transient British Prime Minister, it regarded itself as negotiating with the U.K. government," added Rutter.

Since agreeing a draft withdrawal plan with May, European Union leaders have consistently claimed that talks will not be reopened.

Just last week, Jean-Claude Juncker revealed that he was "crystal clear" with Mrs May that "there will be no renegotiation."

Whether the EU can maintain this hard-line stance remains to be seen but regardless of who becomes the next U.K. leader, it seems certain they will be tackling the future relationship with Europe under the guise of the withdrawal agreement already drawn up under Mrs May.

"The withdrawal agreement is there, it's not a Theresa May withdrawal agreement. The UK government has agreed this, and the PM got her cabinet to support it. So, the first issue a new prime minister has to make clear is what are they going to do with the withdrawal agreement that is there," said Rutter.

As they rally support for their campaigns, Conservative prime minster candidates have been circling around three options: Ignore the withdrawal agreement, renegotiate it, or ask parliament again to ratify it unchanged.