Rishi Sunak will head to Rome on Saturday to tackle illegal migration and organised crime in talks with the Italian and Albanian prime ministers.
The latest migrant death in the Channel on Friday underlines the importance of international efforts to "stop the boats", the Prime Minister’s spokeswoman told reporters.
"The Prime Minister’s thoughts are obviously with all those who are affected," she said.
"There is an ongoing French-led investigation, as you would have seen.
"It serves as a stark reminder of how dangerous these crossings are and just how crucial it is that we work together to stop the boats and clamp down on the organised criminal gangs that are fuelling it."
More than 60 people were on board a boat as it began to deflate off the northern coast of France in the early hours of Friday morning, the French coastguard said.
A total of 66 people were rescued and taken to safety within an hour but two people were found unconscious. A woman could not be resuscitated and a second person was flown by helicopter to a Calais hospital in a life-threatening condition, the French coastguard said.
Mr Sunak's talks with Italian premier Giorgia Meloni and Albania's Edi Rama "will be focused on our joint efforts to tackle illegal immigration and organised crime", as well as "other shared challenges such as the war in Ukraine and the conflict in Gaza", the spokeswoman added.
"As you've heard from the Prime Minister direct, he is clear that this is a shared global challenge and it is important that countries work together to address it, just as we are with Rwanda and with other like-minded countries such as Italy and Albania."
A returns agreement with Albania has seen the number of cross-Channel migrants from the Balkan country fall by 90 per cent, the Government says.
Asked whether a broader deal to process asylum seekers in Albania could be up for discussion, following setbacks for the Rwanda deportation scheme, the Prime Minister's spokeswoman indicated the focus would rather be on our "existing partnerships" with both Italy and Albania.
Mr Sunak this week survived a high-stakes Commons vote over his troubled Rwanda plan, and Foreign Secretary James Cleverly has said it is not the only potential tool available to combat the illegal boat crossings.
Mr Cleverly said the Government would go further on the crisis after the migrant died and another was left in a critical condition in the latest sinking of a boat in the Channel.
"The incident in the Channel last night is a horrific reminder of the people smugglers’ brutality. 25,000 people have been averted from crossing this year – but we must and will do more," he wrote on X, formerly Twitter.
The Refugee Council’s chief executive Enver Solomon said it was "yet another terrible and avoidable tragedy", adding: "These appalling deaths are becoming too common and there is an urgent need to put in place safe routes so people don’t have to take dangerous journeys across the world’s busiest shipping lane.
"Instead, the Government is pushing ahead with its unworkable and unprincipled Rwanda plan as well as shutting down existing safe ways to get to the UK."
French authorities confirmed two people had died in a similar incident off the coast of France last month.
Two others died after trying to cross the Channel in separate incidents in August and November 2021, while an inquiry was launched last month after 27 people died when an inflatable boat capsized, also in November 2021.
More than 29,000 migrants have arrived in the UK this year after crossing the Channel. This is the second highest annual total to date since records began in 2018.
