May reveals that in her meetings India, Mexico, South Korea and Singapore all said they would "welcome" talks on removing trade barriers.
New British leader Theresa May sought Monday to start shaping her country's post-EU access to world markets, but faced a Japanese warning over the fallout from Brexit while the US said London was not its priority.
In the wake of its vote to leave the European Union, Britain must renegotiate its access to world markets, an issue currently handled by Brussels.
It is a huge task for the world's fifth biggest economy.
May met Australian Prime Minister Malcolm Turnbull on the sidelines of a Group of 20 summit in China, who said that Australia had "already been engaged in discussions with you about what the free trade agreements may look like" following Britain's EU exit.
May revealed that in her meetings India, Mexico, South Korea and Singapore all said they would "welcome" talks on removing trade barriers.
That could upset European leaders, after EU commission chief Jean-Claude Juncker said he opposes trade talks between Britain and other economies while it remains part of the European Union.
"I don't like the idea that member states of the EU, including those who are still a member state of the European Union, are negotiating free trade agreements," he said on Sunday.
Such discussions were an "exclusive matter" for the European Union on behalf of its members and "we are sticking to it", he told reporters.
According to EU officials, formal negotiations with Brussels itself cannot start until London triggers Article 50, the treaty provision governing its up to two-year-long departure from the grouping.
The uncertainty is weighing on businesses and investors. When May met her Japanese counterpart Shinzo Abe on the sidelines of the summit he asked that she ensure the environment for Japanese companies remains as "transparent and predictable as possible", a Japanese official told AFP.
The comments came after Tokyo delivered a strong warning about Brexit.
More than 1,000 Japanese companies employing some 140,000 local people do business in Britain -- many of them lured by the access the country offers to the EU and its single market of hundreds of millions of consumers.
Some of Japan's best-known companies, including Toyota, Hitachi and investment bank Nomura, were re-assessing their investments after the shock referendum result in June, the Tokyo government said.
"We strongly request that the UK will consider this fact seriously and respond in a responsible manner to minimise any harmful effects on these businesses," it added.
Japan's direct investment in the country has topped 10 trillion yen ($96 billion) to date.
Not a priority
Australia will help Britain conduct trade talks, Turnbull said Sunday, as London has not had to hammer out its own deals since joining the EU and lacks experienced negotiators.
Britain maintains a close relationship with its resource-rich former colony, and May said she was grateful for Turnbull's offer of trade discussions.
Australia would be "one of the first countries we will be looking to" and Canberra's trade minister will visit Britain this week for exploratory talks, May said.
"We will be looking to establish new trading relationships around the globe," she said.
But US President Barack Obama warned that ahead of British talks, Washington's priority would be on putting its Trans Pacific Partnership trade agreement into effect and settling negotiations on a transatlantic deal with the European Union known as TTIP.
"Those negotiations are proceeding, and so it would not make sense for us to put these efforts aside," he said Sunday.
The two countries aimed to "ensure that we don't see adverse effects" in their commercial ties.
But Before the referendum vote Obama warned Britain would be at "the back of the queue" in negotiating a trade deal with the US.