Dr Fox wrote that dozens of countries are lining up to sign bilateral trade deals with the UK
The International Trade Secretary said work was already being carried out with "a number of countries" to see how barriers to commerce and investment could be removed.
Dr Fox said the UK would champion free trade in a world where decades of progress to open up markets was under threat.
Although the UK cannot strike bilateral deals while a member of the EU, The Daily Telegraph reported that informal negotiations had already begun with 12 countries.
The UK is no longer 'at the back of the queue'
Writing in the newspaper, Dr Fox said: "Trade ministers have visited 55 countries, promoting UK exports of goods and services and encouraging investment.
"Since the referendum, more than £16 billion has been invested in the UK from overseas; a clear vote of confidence.
"At the same time, we are exploiting new trade opportunities and discussing the possible shape of new agreements once we have left the EU.
Trade Mininsters are currently in negotiations with at least 10 countries for post-Brexit deals
"While we remain members we will fulfil our current commitment to push forward trade deals with Japan and Canada, and support international agreements on services and environmental goods.
"But when we leave, we will want to develop new arrangements with countries such as Australia, New Zealand and India.
"We are conducting trade audits with a number of countries to see how we can remove barriers to trade and investment to our mutual benefit."
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Boris Johnson's meeting with US officials gave positive signals for a post-Brexit UK-US deal
Prime Minister Theresa May has said the UK will leave the single market and has ruled out retaining full membership of the customs union – which ministers hope will give the country the freedom to secure trade deals.
Dr Fox said: "Since joining the EU, trade as a percentage of GDP has stagnated in the UK.
"That is why it is time for Britain to get out into the world and rediscover its role as a great, global, trading nation.
Dr Fox wants to forge new deals with anglophone countries and developing economies such as India
"Dozens of countries are preparing to expand their trading links to the UK.
"As the Foreign Secretary discovered when he visited the United States, the UK is no longer 'at the back of the queue' with our largest single trading partner.
"This Government will never compromise on the prosperity of the UK. We see that Brexit is not a threat to that prosperity, but the key."