Keir Starmer has arrived in Canada to set out his doctrine for tackling international threats at a gathering of world leaders, the latest step in the Labour leader’s move to flesh out policy in politically turbulent areas such as immigration. Amid continued efforts by Starmer and his team to push back against the “nonsense” that closer cooperation with the EU would involve the UK having to accept 100,000 asylum-seekers a year, the Labour leader was in Montreal for the Global Progress Action Summit of centre-left politicians. After expected talks with Justin Trudeau, the Canadian prime minister, among others, Starmerwill travel to Paris next week to meet the French president, Emmanuel Macron, with refugees and small boats likely to be on the agenda. The diplomatic and media blitz for Starmer, who is joined in Canada by David Lammy, the shadow foreign secretary, will also include appearances on the Sunday morning political shows. With an election potentially less than a year away, Starmer is aiming to use the Montreal summit to set out his proposals on asylum in the context of what he has termed an “axis of instability”, also taking in other cross-border issues like the climate emergency and terrorism. After spending Thursday in The Hague talking to officials from the EU’s law enforcement agency, Europol, about cross-border cooperation on stopping people-smugglers, Starmer said he wanted an EU-wide returns deal and was willing to discuss the UK accepting a quota of people in return. The comments sparked 24 hours of attacks from Conservative MPs, who claimed Labour’s plans could result in an extra 100,000 people coming to Britain from the EU every year. There was also some disquiet from a few Labour MPs about Starmer’s pugnacious language in an article for the Sun, where he said those who disagreed with proposals such as treating criminals involved in cross-Channel people-smuggling as terrorists were “un-British”. Yvette Cooper said on Friday that the claims about 100,000 arrivals year were “fiction”. The shadow home secretary said her party would not sign up to be a member of the official EU quota system, under which countries have to take an agreed share of people or pay €20,000 (£17,200) for each person they refuse to take. “What we are talking about is having a negotiation around a returns agreement where, for example, we think that should look at family reunion for children who have family in the UK who currently have no safe legal route to be able to join that family in the UK,” she told BBC Radio 4’s Today programme. “As a result they end up on these boats, they end up being exploited by these criminal gangs.” Starmer’s hope is to shrug off such criticism and present cooperation with the EU over unofficial Channel journeys as a more grownup and confident approach, contrasting this with what he will say is the Conservatives’ inability to cooperate internationally. The other aim is to set out a robust response to global issues as a strength for left-leaning parties, with a Labour aide telling the Times on Friday: “Border security is a progressive cause.” Nevertheless, some on the left have criticised Starmer’s recent promises to “smash” criminal people-smuggling gangs. Steve Smith, the chief executive of Care4Calais, told the Guardian: “‘Smash the gangs’ may get him a headline in the Sun, but it’s not a plan.”