Brexit will bring “a huge series of upsides” for the UK in international trade, Dominic Raab has promised at the start of a symbolically important trip to North America, during which he will press the White House about the need for a rapid deal.

The foreign secretary is expected to meet the US vice-president, Mike Pence, in Washington late on Tuesday, and to hold talks with his counterpart, Mike Pompeo, on Wednesday. He will then travel to Mexico.

Raab, a die-hard leave supporter, will be conscious of the need for positive words from Washington on a quick post-Brexit trade deal as a counterpoint to warnings over the likely economic impact on the UK of a no-deal departure from the EU.

A powerful group of Congress members warned last week that they would block any trade deal with the UK if Brexit affected the Irish border and jeopardised peace in Northern Ireland.

The UK’s emphasis on a US deal was further illustrated with the news that the international trade secretary, Liz Truss, would also visit the country this week. She is to meet trade groups, officials and Congress members over four days, her department said.

The former US Treasury secretary, Larry Summers, however, said on Tuesday that he did not believe a “desperate” UK would manage to secure a good post-Brexit trade deal.

Summers, who was a senior official under Bill Clinton and Barack Obama, said the UK was in a weak position when it came to negotiating with trade partners.

He told BBC Radio 4’s Today programme on Tuesday: “Britain has no leverage, Britain is desperate … it needs an agreement very soon. When you have a desperate partner, that’s when you strike the hardest bargain.”

Before his US meetings, Raab met the Canadian foreign minister, Chrystia Freeland, and talked up the countries’ future trade prospects in glowing if vague terms.

After the meeting in Toronto, Raab was bullish about the effects of leaving the EU, telling the BBC: “There’s a huge series of upsides from Brexit, particularly with a more ambitious and energetic approach to our global role.”

He reiterated Boris Johnson’s warnings about a likely no-deal departure if the EU declines, as it has always said it will, to rewrite the withdrawal agreement and ditch the backstop insurance policy for the Irish border, saying: “We want to get a deal with the EU, but we’re going to be leaving if there’s no movement from their side at the end of October, come what may.”

In comments before a news conference with Freeland, Raab said the UK wanted “to ensure that everything possible is in place to ensure continuity of trade after Brexit”.

He said: “Chrystia and I agreed on the need for seamless transition. We’re going to be looking into taking that work forward with officials in our teams in the weeks ahead in the run-up to the end of October.

“I’m pleased to be able to say in Canada that, for the UK, Brexit is not just about risk management, although that’s important and I wouldn’t want to be glib or not take that very seriously. But it is also – and our prime minister has been very clear about that – about grasping the enormous opportunities of our two countries.”

Raab focused heavily on trade, but Canadian coverage of the event centred mainly around Freeland seeking UK support over the detention of two Canadian nationals in China, part of a series of tensions between Ottawa and Beijing.