"It is frustrating that we have not yet brought this process to a successful and orderly conclusion", May wrote in her letter requesting a deadline extension to Donald Tusk, president of the European Council, which is comprised of the heads of states of EU members.
"A senior European Union official said Donald Tusk had described a flexible extension as "the only reasonable way out" during a long meeting with officials' yesterday evening ahead of the 10 April summit". "The United Kingdom Government remains strongly committed to doing so, and will continue to act as a constructive and responsible Member State of the European Union in accordance with the duty of honest cooperation throughout this unique period".
With Britain due to leave the bloc on April 12 and no sign of her minority government being able to pass a deal through parliament on its own, May turned to Labour Party leader Corbyn in recent days in the hope of securing a bi-partisan agreement.
After a seven-hour meeting with cabinet ministers on Tuesday, Theresa May announced she would request a "short" extension to Article 50 and reach out to Leader of the Opposition Jeremy Corbyn to try and reach an accord on her proposed withdrawal agreement, which has now failed to attain a majority vote in the House of Commons three times.
The UK is now due to leave the European Union on April 12 and, as yet, no withdrawal deal has been approved by MPs.
Any extensions have to be agreed by all 27 member states of the EU.
May badly needs evidence of a viable divorce strategy to persuade the other 27 European Union leaders at a summit next Wednesday to grant a delay, preferably on her preferred departure date.
"The fact is that on Brexit there are areas where the two main parties agree: we both want to end free movement, we both want to leave with a good deal, and we both want to protect jobs".
Ministers and Labour officials are holding a third day of talks created to establish whether they can unite around a compromise Brexit plan under which the Withdrawal Agreement would remain unchanged, but with changes being made to the accompanying Political Declaration on future relations.
She is now racing against the clock in a desperate bid to get her proposals approved in time for the Brussels summit so that Britain can avoid taking part in the European vote. May said in a letter sent on Friday to Donald Tusk, the head of the European Council that represents EU leaders.
The prime minister also said in the letter that if talks with Labour don't lead to a "single unified approach soon", she will attempt to establish a "consensus" on options on a future relationship that could be put to the Commons.
Several of May's ministers have warned that a long extension will be the only thing on offer.
"Talking about an extension is a bit premature as the 27 had set a clear condition that the request must be justified by a clear plan", le Figaro quoted as saying a source from President Emmanuel Macron's office, the Elysee. They voted it down for a third time last week.
Sir Keir said: "So far, the Government isn't proposing any changes to the deal".
From both sides, it sounds like they are serious and genuine, and negotiators got into the guts of both their positions and technical details on Thursday. However, Ms. May has repeatedly ruled out remaining in the customs union because it would mean the United Kingdom would be unable to pursue its own trade policy since members of the customs union must apply the same external tariffs.