Svalbard at the time was owned by Russia, if I'm not mistaken

For the most part, the main reason Russia even considered selling Alaska to the states was because it wasn't worth it. Svalbard meanwhile gave easy access to whaling and mining, things that Russia (a country which was relatively behind in the Industrial revolution desperately needed). Meanwhile Iceland, a country ruled by Denmark, would have had tons of diplomatic relations with the UK and selling it would've been easier.

No way in hell the British could but Svalbard. Plus, according to Endless' archives, there was natives in the area where Frostpunk takes place. Iceland has natives, but Svalbard is a desolate Icey wasteland with practically zero life, like Finland