A deal between the countries was announced in December and ratified in Bern, Switzerland on Monday.
Deals with Australia and New Zealand have been signed, but they are mutual recognition agreements - meaning the two sides will replicate aspects of the existing arrangements with the European Union - rather than free trade deals.
Signing the agreement in Bern today, global trade secretary Liam Fox said: "Switzerland is one of the most valuable trading partners that we are seeking continuity for, accounting for more than £32bn worth of trade a year".
The formal signing of the deal, on which agreement had previously been announced, is one of only handful of concrete steps Britain has made towards ensuring that all the trade deals it now benefits from as an European Union member will continue after it leaves the bloc next month.
The UK's exit from the bloc may lead to a return of a hard border between the Republic of Ireland and Northern Ireland in potential violation of the 1998 Good Friday Agreement, which specifically stipulates that no physical border should exist between the two sides.
On Sunday, the director-general of the Confederation of British Industry (CBI) said the government's failure to secure other continuity of trade deals was an "emergency".
But in an effort to see off attempts to bind the Government's hands, Downing Street is promising another opportunity to table amendments - which are likely to include measures aimed at taking a no-deal Brexit off the table - on February 27.
A customs union is one of the demands made for any deal to get Labour support.
The EU has thus far insisted that it will not reopen negotiations.
"It is not going to be easy but crucially President Juncker and I have agreed that talks will now start to find a way through this, to find a way to get this over the line and to deliver on the concerns that parliament has so we get a majority in parliament". "MPs can not be sure precisely what future relationship it would lead to", May wrote.
'We know that businesses are leaving the country, we know that businesses are making plans that will damage communities across the country and just this week we had a new chapter in the unfolding nightmare that the trade deals that the United Kingdom businesses enjoy through the European Union will not be ready in time for leaving'.
"I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deals?" she wrote. The previous similar debate on January 29 was on a motion which simply asked lawmakers to agree that they had considered May's latest statement on the Brexit negotiations.