Trade with Switzerland is worth around £32 billion a year and the rollover of the arrangements come as Dr Fox is under pressure to secure continuity for other existing European Union deals.
She hopes to get Brussels to agree to revisions, but so far the European Union, with the united support of all the other 27 member countries, has refused to reopen negotiations on the text of the 585-page agreement.
It was signed, in the Swiss city of Bern, by International Trade Secretary Liam Fox and the Swiss federal councillor Guy Parmelin.
But a study published early previous year by research firm Cambridge Econometrics estimated that a total of 500,000 British jobs would be at risk if there is no deal.
In 2017, Switzerland registered 11.4 billion Swiss francs (US$11.4 billion) in exports to Britain, making it the wealthy Alpine nation's sixth largest export market.
They have also signed a deal to preserve the rights of some 43,000 British nationals living in Switzerland and the 35,000 Swiss living in Britain after Brexit.
British businesses are also stockpiling goods as March 29 draws nearer, when the United Kingdom will by default crash out of the block if a withdrawal agreement can not be reached. But a member of May's cabinet pledged Sunday to give parliament a further ballot two weeks later - a measure meant to give the premier more time for talks with the EU.
And there were signs of unease in Tory ranks at the idea of Mrs May exploring means of bringing the Labour leader on board in her search for a Brexit deal.
Britain and Switzerland will sign an agreement on Monday to continue trading on preferential terms after Brexit, the British trade department said, protecting a trade relationship worth 32 billion pounds, Trend reported citing Reuters.
"I'm certain of one thing, is that it's not going to be as good as if they had not been Brexit, that is for sure", Lagarde said.
Switzerland meanwhile is Britain's fifth biggest export partner outside the EU.
She is unlikely to signal any shift towards a closer future relationship with the EU, after writing to Jeremy Corbyn to underline her continued objections to a customs union, and instead she will focus on the backstop.
The effort is aimed at ensuring Britain does not leave the European Union March 29 without a trade deal, a disorderly exit the Bank of England has warned could throw the British economy into recession. He says May's agreement can achieve "a great deal of what Jeremy Corbyn is interested in without taking away that option of having other trade deals".
"We have got what we call the Political Commission that simply does not take its orders from democratically elected governments".