Other than first king of the north and the first king of the south (according to WT interpretation and according to the interpretation of many Christian groups), I think it also pertains to the role the most recent kings take in relation to the prior two kings. I think it is role which primarily identifies them, not primarily which one is at the most northern latitude. For a WT explanation in regards to the communist block led by the Soviet Union (now identified as led by Russia and its allies) being the king of the north, see pages 270 and 275-278 in the WT 1999 book called Pay Attention to DANIEL'S PROPHECY (note that book was revised in 2006 but I don't have a copy of the revision and I haven't read the current online edition).
But note that most modern scholars (at least according to https://en.wikipedia.org/wiki/Daniel%27s_final_vision ) say "... that the Daniel who appears as the hero of the Book of Daniel never existed ...".
If one accepts the WT's interpretation (at least that given in the first edition of the Daniel book) of the current kings of the north and the south (and of whom they currently say is the king of the north), then most likely according to that interpretation there will not be a nuclear war between Britain-USA and Russia (along with its allies). Why is that? Well if they mutually attacked each other with nuclear weapons then most likely neither of them would remain a world power and there would likely no longer be a king of the north and a king of the south (in the sense of the WT interpretation of the prophecy in Daniel) - not even later replacement kings for them. But page 285 (along with page 179) of the WT's book on Daniel says that neither of the two kings comes to its end by the hands of the other, but that instead the king of the south is destroyed by God's Kingdom and that at the battle of Armageddon all earthly kings at time will be removed by God's kingdom.
Interestingly page 278 of the WT's Daniel book in paragraph 17 says the following. "In modern times [Edom, Moab, and Ammon] represent nations and organizations that the king of the north targeted but was unable to bring under his influence." Could that also prove to be the case with Russia's attack on Ukraine? Very recent reports says that Russian is having a hard time in quickly defeating Ukraine, and the reports say many nations are condemning Russians war actions against the Ukraine. Furthermore Germany and the USA announced it will send weapons to the Ukraine, the EU said it will pay for weapons that will go to Ukraine, nations are financially cutting off Russian banks from SWIFT, and England along with the EU are cutting off commercial flights to their lands from Russia. Furthermore, according to Fox News "Ukrainian military official releases video showing what appears to be Russian missile system being destroyed by a drone" (but I don't yet know if that claim is accurate).