Liam Fox has admitted crying with pride as the UK voted to leave the European Union (EU).
The International Trade Secretary said the Government had a "duty" to implement the will of voters but refused to guarantee the Brexit process would be completed by the 2020 general election.
Dr Fox insisted the UK would automatically be a member of the World Trade Organisation (WTO) after leaving the EU and pointed to the US as a country which was able to do business with the European bloc without benefiting from the customs union.
In a hint he would not put retaining being part of the customs union at the heart of his post-Brexit plans, Dr Fox told a fringe event at the Conservative Party conference in Birmingham: "Most businesses in the world are outside the European Union.
"The United States is outside the European Union, it does not seem to be seriously hampered in doing business with Europe because it is not in the customs union.
"Again, you have to be rational about all of that."
The customs union allows the free movement of goods with no tariffs but imposes administrative and tariff barriers at its external borders.
Leaving the EU customs union could hit exporters attempting to sell into the remaining members of the bloc.
Dr Fox dismissed the suggestion he was advocating a "hard Brexit" with minimal links to the EU.
"People say 'do you want soft Brexit or a hard Brexit' as though we are talking about a boiled egg.
"What we need to do is to work out the model that we want, set out our timing, set out the process."
Dr Fox played a prominent role in the Leave campaign and spoke of his pride at voters in rejecting the Remain camp's tactics, which were dubbed Project Fear by critics.
At the fringe event hosted by Huffington Post UK, he said: "I'm sure I wasn't the only one who was really quite tearful when David Dimbleby said 'that's it, the British public have voted to leave the European Union'.
"I just felt that given all those big international organisations who had been telling us how bad it would be if we left, I have never actually felt so proud of my fellow countrymen and women as I did at that moment."
Theresa May has said she will trigger Article 50 - which begins a formal process for leaving the EU expected to last two years - by the end of March 2017.
But Dr Fox refused to guarantee the process would be completed by 2020.
He said: "When you get up in the morning, the most important thing is not walking out the door, it's what you do with the rest of the day.
"That's what we need to focus on, we need to focus on that long-term relationship and what we want the country to be.
"Like the Prime Minister, I would not put a timescale on it. That's one of the cards that we have in our negotiation, why would we want to hand it over at the outset?"
He dismissed the concerns raised by company bosses, including Nissan's Carlos Ghosn, about continued investment in the UK due to the uncertainty of Brexit.
The UK benefited from its legal framework, skilled workforce, low regulation, low tax regime, the use of English and its strategic time zone - none of which depended on the EU, Mr Fox said.
He added: "The point I have been making when I have been talking to CEOs elsewhere is that if it's not going to be Britain, where else do you choose?
"You tell me anywhere else that has all those natural advantages and doesn't have the disadvantage of the potential economic instability of the eurozone?
"Investment is a balance of risks when you come to look at it and I think that the UK remains the number one destination for safe investment."
Dr Fox warned of the possibility of other countries following the UK's lead unless there were changes in the EU.
He said: "We don't want there to be a domino effect across Europe.
"But European leaders need to understand that a lot of people are dissatisfied with the way the project is being run."
In a swipe at David Cameron, Dr Fox criticised the former prime minister's order for the civil service not to prepare for Brexit.
"I happen to think that during the referendum some of that work should have been done in case there was a leave vote," he said.
"The idea that civil servants were banned from doing that work was a very big mistake."
Dr Fox said his department was "making the preparation for one minute past midnight" on the day the UK leaves the EU and "we will move into that different environment".
That would mean the UK claiming its place in the WTO: "It is not a question, as I have read in a lot of the press, of will Britain reapply for WTO membership, we don't have to do that.
"But what we do have to have are schedules under which we operate.
"It may well be that we would want to replicate those EU schedules and look at those as the basis on which we have our licence to trade."