The audit said uncertainty over the course of the negotiations has delayed preparations for a no-deal scenario, with organised crime gangs potentially stepping in to smuggle goods across the new EU-UK frontier.
Time has run out for the government to complete all of the preparations needed to ensure the United Kingdom border is fully operational in time for a no-deal Brexit by March next year, the National Audit Office has warned.
Mrs May added that protecting the UK's integrity was so important that she had a duty to explore "every possible solution" in keeping the Irish border open and ensuring that there are no new barriers between Northern Ireland and the rest of the UK.
"That withdrawal agreement is 95 per cent agreed and written, so it's the detail work around how we protect Ireland, the island of Ireland as a whole and the border issue and I believe there is a landing zone we can work towards that Britain can live with and we can accept".
In its report, the National Audit Office said that political uncertainty and delays in negotiations with the European Union have hampered preparations for new border arrangements, and the government is now racing to bolster computer systems, increase staffing and build new infrastructure to track goods.
"We still regard a last-minute deal as the most likely outcome but due to recent events we now estimate the chances of a âhard Brexitâ as nearly as high as the base case". But as the Brexit deal nears, the pressure is growing on her critics to put up or shut up.
She's also opposed by pro-EU lawmakers who want to keep close ties with the bloc after Brexit.
These hardliners - a big enough group to trigger a leadership challenge but not big enough to bring May down - continue to press for an alternative model and downplayed the importance of the border problem. Weekend newspaper headlines saying the prime minister is entering "the killing zone" and faces a metaphorical knifing drew sharp rebukes.
May did not address the quote directly, but said: "It is incumbent on all of us in public life to be careful about the language we use".
In a bid to calm passions, May will address MPs in the House of Commons on Monday where she will say the divorce deal with Brussels is almost done.
"The chairman of the 1922 Committee [Graham Brady], when he receives that many letters, has to hold a ballot". Although the government has achieved much and its planning efforts have increased in momentum, given the scale of the task, there are inevitably gaps and risks to its progress. "But she operates at the upper end of that scale nearly every day of her life and remarkably, walks out at the other end".
She argued that her strategy for pulling Britain out of the European Union was "not about me" but based on the "national interest"..
In a report on the eurozone issued yesterday, the International Monetary Fund (IMF) said Ireland would be the country hit hardest by Brexit.