The Prime Minister was in Rome meeting Italian counterpart Giorgia Meloni, whose approach to border control has witnessed a 60% drop in arrivals by sea over the past year.
Sir Keir said this was "likely attributable to the work the Prime Minister has done upstream" by preventing people from travelling in the first place.
The Italian success is widely attributed to controversial deals struck with north African nations, including Libya and Tunisia, from where most migrant boats depart.
Sir Keir added: "I have always made the argument that preventing people leaving their country is far better than trying to deal with those that have arrived. I was very interested in that. In a sense, today was a return - if you like -to British pragmatism."
Deterrent
Ms Meloni confirmed the pair also discussed the Albanian scheme.
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