Denis MacShane is a former British minister for Europe and author of Brexit: How Britain Will Leave Europe. He is a special adviser at Avisa Partners in Brussels.

With Britain having voted to leave Europe, will Canada come to the rescue and make the Atlantic narrower than the Channel?

To judge by the boosterism from pro-Brexit British ministers that new Prime Minister Theresa May has appointed, a free-trade deal with Canada will be just the ticket once Britain loses its right to trade freely in the single European Union market of 500 million middle-class consumers.

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Liam Fox, a devotee of Margaret Thatcher and a strident anti-European, has been brought back from the backbenches to be Ms. May's trade minister. He wasted no time in telling the London Sunday Times that he'd already had "very fruitful" trade talks with Canada and that "we have already had a number of countries saying 'We'd love to do a trade deal with the world's fifth-biggest economy without having to deal with the other 27 members of the EU.'"

In fact, France has just overtaken Britain to become the world's fifth-biggest economy, but news arrives slowly in Brexitland. Legally, Britain can't do a trade deal with Canada, North Korea or anyone else until it has fully and finally quit the European Union, since under its treaty obligations, it's the EU, not individual member states, that concludes trade deals.

There is the proposed Canada-EU free-trade deal, CETA, but it has to go through ratification by 28 EU national parliaments. After the upsurge in British dislike and distrust of Brussels officialdom, the legendary "Eurocrats" may prove tricky.

But at least Canada, under energetic Trade Minister Chrystia Freeland (globally, the best-known Canadian cabinet minister after Prime Minister Justin Trudeau), is working hard to promote trade deals.

Three hundred Canadian government trade experts work on these deals around the clock – they take years to negotiate and ratify and can bring down governments. Britain doesn't have a single professional civil servant who is an expert on trade deals. While London is home to the world's best foreign, defence and European policy think tanks, such as Chatham House and the European Council on Foreign Affairs, you would be hard-pressed to find a British think tank on trade or a university professor of trade capable of advising government on what to do.

British-Canadian trade is already strong. Canada runs a healthy balance of trade surplus with Britain, exporting twice as much as it imported in 2015, and there are no visa requirements for British or Canadian citizens to travel across the Atlantic.

The Brexit campaigners would like EU citizens to need visas or work permits before coming to Britain, and when food-safety and animal-welfare campaigners get their teeth into the debate over what subsidies British farmers should receive and what food products can and cannot be imported into Britain, the chances of Britain finding all sorts of new barriers to trade are high.

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As the government laconically notes, there are "difficulties for U.K. law firms to do business due to heavy regulation" in Canada and "agriculture is protected, which can affect imports."

None of these are likely to be wished away just because Britain has said goodbye to Europe and hello to Canada. Indeed, more than four million Brits have signed an online petition to the House of Commons asking for a debate on a second referendum and there is a rising sense that voters were not told about the full economic consequences of Brexit.

Whether Britain stays or shuts the door on Europe, trade and other friendly relations with Canada are vital. But Canada should be careful not to find itself used as a pawn by exuberant Brexiters as they proclaim a wonderful new world of free trade between the two nations. That is not going to happen soon, and it will inevitably be limited by caveats, as all who lived through the early days of the North American free-trade agreement are aware.

Brexit's ambassadors should make their own case for latter-day isolationism, without trying to drag Canada into their domestic politics.