Fox announced Britain had launched an informal working group with Latin America's second-largest economy seeking to "ensure all the preferential arrangements that the UK currently enjoys with Mexico remain in place."
Britain is walking a delicate line as Brexit talks inch forward in Brussels.
It will be ousted from all EU trade deals when it leaves the bloc -- scheduled for March 2019.
But EU rules prohibit it from negotiating new deals until then.
Fox's Mexico trip comes on the heels of a visit to the United States, where President Donald Trump this week hailed the prospect of a "very big" trade deal with Britain.
Foreign Minister Boris Johnson was meanwhile on a tour of the Asia-Pacific region, visiting Australia and New Zealand after a trip last week to Japan.
Fox insisted Brexit would make Britain more open to trade, not less.
"For the first time in more than four decades, the United Kingdom will enjoy a fully independent trade policy, free to build closer ties around the world with partners old and new," he told a breakfast meeting of business leaders in Mexico City.
He said he and Mexican Economy Minister Ildefonso Guajardo, who held talks over dinner yesterday, agreed on the need to champion free trade and "reverse a rising tide of protectionism."
Mexico is also keen to explore new trade relationships as talks loom on overhauling the North American Free Trade Agreement (NAFTA) with the United States and Canada, a major driver of its economy for the past two decades.
Mexico's economy, which is second only to Brazil's in Latin America, relies heavily on its preferential access to the United States, the customer for 80 percent of its exports.
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