With a POD after 1900, make the Faroe Islands part of the United Kingdom, either by making it a crown dependency or a county of Scotland.
Central Powers victory with vassalised Denmark also might do it.
That was pretty much the actual situation post WWI - at least if you ask Redbeard (and the P.Munch) policy of not offending Germany and lying dead made it factual.
Rather a 1917 German occupation of Denmark and Norway with a defeat in the end could see a British occupation and no return of the islands. A Danish lying dead or inviting in German occupation forces would be seen in a much different light than in 1940!
And then there'd be no 1920 return of North Schleswig.