But if the UK remains in a customs union with the EU, its prospects would be ruined, he warned.
Dr Fox’s impassioned speech in the City of London came in response to Jeremy Corbyn’s U-turn on Europe this week.
The Labour leader said on Monday that his party now supports tying Britain to Brussels rule in a customs union.
Dr Fox told an audience of business leaders that remaining in such an arrangement with the EU after Brexit would be “a complete sell-out of Britain’s national interests”.
He described Mr Corbyn and Left-wing Remainers as “imbeciles” who would put public services at risk.
He said being in a customs union which allowed the EU to set trade rules would let Brussels impose deals which forced the government to hand over public services like the NHS to private companies.
Labour has previously expressed fears that an EU deal with the US would allow American firms to become involved in UK health care provision.
Dr Fox said: “Those on the political Left who opposed TTIP (the agreement between the European Union and the United States) might want to consider that in a customs union, they would have to implement any elements of TTIP, whether they like them or not, in any sectors.”
His words came amid new evidence that Britain’s economy is booming with the latest YouGov/Cebr Consumer Confidence Index standing at 108.7 this month, up from 108.5 in February.
Dr Fox said that outside a customs union the UK could join the North American Free Trade Agreement (NAFTA) or set up bilateral agreements with other countries, generating massive wealth for the UK.
Outlining the future, he argued: “We cannot let the practices and patterns of the past constrain the opportunities of the future. We require an economic outlook that allows us to take advantage of the substantial opportunities that Europe will continue to bring, but without limiting our ability to adapt to a changing and growing world beyond the European continent.
“The UK is perfectly placed to partner with the economic powerhouses of the future, and they in turn are eager for the mutual prosperity that such a partnership would bring.”
But he warned: “To do this, we need the ability to exercise a fully independent trade policy.
“We have to maximise our overall trading opportunities for the UK and secure the prosperity of our people.”
He hit back at Sir Martin Donnelly, permanent secretary in the Department for International Trade until last year, who this week criticised the idea of free trade agreements.
Dr Fox said: “It is unsurprising that those who spent a lifetime working within the European Union would see moving away from the European Union as being threatening.”
Leave Means Leave group co-chairman Richard Tice said: “Dr Fox clearly understands that Britain will only enjoy the full economic benefits of Brexit and help the least well off in society when we can cut trade tariffs.”