This was a radical and fantastic idea of Palmerston's, which led to vigorous debate.
But the interest in Palmerston's case going against Portugal and hunting the slave ships with the intent of ending the slave trade. That's what he felt was England's interest.
Other things Palmerston cared about was that no country would end up powerful enough to dominate the entire world-- that's another thing he saw as part of England's interest. How sad to reduce interest to economic concerns or maintaining traditional alliances, when the idea was initially to justify this act of going against Portugal and the traditional alliance.
"Countries" as such do not have interests, no. This is a line the ruling class puts out when it wants to obscure the fact that its own interests are always prioritized, often to the great detriment of the vast majority of the country.
One could perhaps say that "governments" have interests, and in that case the interests of a genuine socialist state and an authoritarian regime that's just pretending to be one are quite different.
Governments have interests, people have interests, both are interested in the future of their country, which is just land.
This is why I am careful to delineate my patriotism as to my country, land and people, but specifically not my corporate government, who are greedy, genocidal, parasitic traitors to the Constitution and to humanity. A kangaroo court controlled by organized crime.