David Frost used a major speech in Brussels on Monday to state that Britain will not accept EU supervision to create a "level playing field".
The move comes after France warned the two sides would "rip each other apart" in trade talks ahead of the UK's scheduled exit from a Brexit transition period at the end of this year.
Mr Frost said: "It is central to our vision that we must have the ability to set laws that suit us."
"To think that we might accept EU supervision on so called level playing field issues simply fails to see the point of what we are doing.
"It isn’t a simple negotiating position which might move under pressure – it is the point of the whole project."
He said that is the reason there will be no extension to the transition period past the end of the year, because "at that point we recover our political and economic independence in full - why would we want to postpone it?"
The speech follows comments by French foreign minister Jean-Yves le Drian, who predicted a bruising battle between the UK and EU on a post-Brexit deal.
Speaking at the annual Munich Security Conference, he made clear that Brussels will defend its interests when negotiations begin next month.
"I think that on trade issues and the mechanism for future relations, which we are going to start on, we are going to rip each other apart," he said.
"But that is part of negotiations, everyone will defend their own interests."Mr le Drian, a close ally of president Emmanuel Macron, is the latest senior EU figure to warn that the negotiations will be difficult.
Mr Frost added that the UK is seeking an "open and fair" arrangement with the EU based on Free Trade Agreement (FTA) precedents.
"How would you feel if the UK demanded that, to protect ourselves, the EU dynamically harmonise with our national laws set in Westminster and the decisions of our own regulators and courts?"
"The reason we expect - for example - open and fair competition provisions based on FTA precedent is not that we want a minimalist outcome on competition laws.
"It is that the model of an FTA and the precedents contained in actual agreed FTAs are the most appropriate ones for the relationship of sovereign entities in highly sensitive areas relating to how their jurisdictions are governed and how their populations give consent to that government."
The EU has repeatedly warned Britain cannot expect to enjoy continued "high-quality" market access if it insists on diverging from EU social and environmental standards.
There is expected to be a particularly tough fight over fishing rights, with the EU insisting continued access to UK waters must form part of any agreement.
Mr Johnson, in turn, has said the UK will act as an "independent coastal state" taking control of its own fisheries.
A Number 10 spokesman said Mr Frost "will reflect on the institution of the EU and look towards the new relationship we are seeking to build".
The spokesman added: "We want a relationship based on friendly co-operation between sovereign equals," and "We are not asking for anything special or bespoke."
He said: "We are seeking a deal that the EU has struck previously with other countries such as Canada."
Downing Street said it was still seeking "quota-free, tariff-free" arrangements - even though Canada's deal does not eliminate all tariffs and quotas.