The head of the International Monetary Fund (IMF), who is a fierce critic of Brexit, was spotted chatting to a fellow delegate as Mrs May delivered her speech at the Munich Security Conference.
Even though Ms Lagarde was sitting in the front row, she refused to look at the British Prime Minister on the podium, preferring instead to watch the speech on a nearby screen.
Rolling her eyes and gesturing to her female companion, she then got up in the middle of the speech and walked out.
Last week the IMF warned the pound will plummet by as much as 20 per cent if Britain leaves the EU without a deal.
It comes after Ms Lagarde denied the organisation’s predictions had been too gloomy, saying Brexit would harm the UK’s future economic growth.
Project Fear dominated the Remain campaign during the run-up to the 2016 referendum, with the IMF joining David Cameron and George Osborne, then Prime Minister and Chancellor, leading the charge.
Before the referendum Ms Lagarde claimed she had “done her homework” on Brexit and said they had not found “anything” positive about a Leave victory.
She said Brexit would spark panic among investors and send shockwaves through the British economy – particularly the property market.
A report by the IMF said: “Markets may anticipate such adverse economic effects. This could entail sharp drops in equity and house prices, increased borrowing costs for households and businesses, and even a sudden stop of investment inflows into key sectors such as commercial real estate and finance.
“The UK’s record-high current account deficit and attendant reliance on external financing exacerbates these risks.
“Such market reactions could sharply contract economic activity, further depressing asset prices in a self-reinforcing cycle.”
None of this has come to pass and the Bank of England, who were also accused to doom-mongering, last month issued a far more positive assessment of Brexit on the British economy.
BoE Governor Mark Carney said: “The Government doesn’t have to worry about the impact on the financial sector because it will be able to withstand and support the economy.
“From the Bank of England’s perspective what is necessary and what we’ve been doing is to make sure we are in a position in the UK, with its huge financial sector, that we can withstand any outcome and we can take advantage of any outcome.
“We have put the banks in position. That’s providing a crucial base, it’s what the people of the United Kingdom should expect from us and it’s what we’ve done.”