Britain expects the EU to "live up to" its undertakings to offer the UK a Canada-style free-tradedeal, foreign minister Dominic Raab said, reiterating that any deal will not require "high alignment" with the bloc's rules.
Mr Raab has said there will be no new checks on goods if the EU sticks to its commitments.
He said will travel to Japan and Australia next week to work on agreeing trade deals and explore "global" opportunities for Britain after Brexit.
Mr Raab said: "We are taking back control of our laws so we are not going to have high alignment with the EU and legislative alignment with their rules.
"We will want to co-operate and we expect the EU to follow through on their commitments to a Canada-style free trade agreement. That's what we are pursuing.
"There is a great opportunity here for win-win."
Taoiseach Leo Varadkar called on British government not to repeat mistakes of the past by putting down "rigid red lines".
Speaking on the BBC's Andrew Marr show, Mr Varadkar said that while the UK's decision to leave is regretted "we totally accept your decision and we're glad that is happening with the Withdrawal Agreement."
He said: "One thing I'd say to everyone is let's not repeat some of the errors that were made in the past two-and-a-half years, let's not set such rigid red lines that it makes it hard to come to an agreement and let's tone down the kind of nationalistic rhetoric.
"As is always the case when it comes to negotiations, setting out so boldly such firm red lines actually makes coming to an agreement more difficult because the other party you are negotiating with doesn't feel they got a fair deal unless those red lines get turned pink or bent in some way."
Mr Varadkar also said there will difficulty over Brexit negotiations if there is trouble forming an Irish government.
"Negotiations will take place between the UK and the EU, but we're very much plugged into the EU side. We're part of the 'Team 27' and we have a lot of influence in that regard as the EU trade commissioner is an Irishman," he added.
Former European Council president Donald Tusk said the upcoming trade talks with the UK would be focused on "damage control".
He said there would be "great consequences" for "both sides" if Prime Minister Boris Johnson decides to move away from Brussels' regulations.
Mr Tusk said: "There is no desire for punishment.
"For Brexit, and the negotiations after Brexit, this is a process of only damage control.
"The problem is, objectively, that there will be some losses and damages, no doubt, on both sides - but not as an intentional 'game'."
He also said he did not think Britain would return to the European Union in his lifetime and called for Remain voters "not to dream about another referendum".
Earlier, speaking to Sky News, Mr Raab said: "We will not be insisting that they (EU) align with our rules as applies to the free trade deal with the UK, that's not the way free trade deals are done globally.
"I'm sure that the EU will want to adhere to their commitment to a Canada-style, best in class, free trade agreement and there's great opportunity there on all sides."
Asked about paperwork for business and customs checks at the border, he said: "The commitment is to avoid all of those things with a best in class free trade agreement and I'm sure - we're committed to it on our side and I'm sure the EU will want to stay committed to the undertakings that they've made. That's what we expect, that's what negotiations are all about."
He said: "We will hold them to account for the undertakings they've made and we'll live up in good faith and with a good spirit of optimism, of good will to get that deal done."
Mr Raab said the EU's chief negotiator, Michel Barnier, was "wrong" to suggest that there would be border checks if the UK diverges from Brussels' rules.
He said talk of checks was "directly in conflict" with both the Withdrawal Agreement and Political Declaration agreed in October.
Mr Raab, asked if Mr Barnier was wrong, said: "Yes. He is wrong. If the EU lives up to its commitment on its side, both in the Withdrawal Agreement and also the Political Declaration."
He added: "We expect those assurances and agreements to be kept to. That's why we've done this deal - it is a package."
Also speaking to Sky News, Northern Ireland's First Minister Arlene Foster said it is difficult to see how there will not be checks between Britain and Northern Ireland in an EU trade deal.
Asked whether she believed Prime Minister Boris Johnson's assertions that there will be no new checks, Mrs Foster said: "It's difficult to see how that is the case given that we've heard from other members of the cabinet that they intend to diverge from single market regulations, whilst Northern Ireland remains within the single market. It's difficult to see how that's going to work."