More than a dozen arrests have been made in connection with the deaths of 27 people who attempted to cross the English Channel in a dingy last November.
National Crime Agency (NCA) officers have been helping the French border police with the operation in France, which has seen 15 people arrested.
It comes after the victims drowned in the boat which sank off the coast of Calais.
Five others were arrested soon after the incident.
More than 3,000 migrants crossed the Channel to the UK in June - the highest monthly total this year.
Some 3,136 made the crossing on 76 boats in the 30-day period, with journeys taking place on 19 of those days, according to PA news agency analysis of government figures.
NCA Deputy Director of Organised Immigration Crime, Andrea Wilson, said: "The events of last November were a tragedy, but in that time our resolve to bring those responsible for these deaths to justice has not diminished.
"We have worked closely with our French partners to identify those who we suspect were involved, and that joint investigation continues.
"It is also assisted by Border Force and Maritime and Coast Guard Agency in the UK.
"Many of those involved in organising these dangerous crossings operate outside the UK, so it is vital we work closely with law enforcement partners in France and beyond to target them.
"This includes having NCA officers based overseas, sharing intelligence and working side by side on joint investigations, as we have done in this case.
"Tackling people smuggling remains a priority for the NCA."
Home Secretary Priti Patel added: "My thoughts continue to be with the families of all of those who tragically lost their lives in this horrific incident.
"The NCA and other agencies across the UK and France will continue their tireless work to deliver justice for the victims and their families by identifying those responsible and ensuring they feel the full force of the law.
"By working together, and through the tough new domestic measures we have just brought into law, we will crack down on the evil people smugglers in our efforts to prevent any more loss of life in the Channel."
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