Yeah.
In the 1930s my maternal grandmother (born 95 years ago) was barred from some jobs* because although born in the UK to a British (English & Welsh) mother, her father was Danish, thus giving her dual nationality should she choose to claim it.
*She discovered this when she applied to join the Metropolitan Police & was turned down because of it.
I didn't think Danes did dual nationality. My mother remains Danish, despite having lived in the UK since 1956. Having been born stateless and acquiring Danish nationality as an adolescent, it's not something she wants to give up.
Current Danish law restricts dual nationality, but does allow it in such cases as that of my grandmother. She was Danish because her father was Danish & married to her mother (& the marriage was registered with the Danish authorities: they even had a Lutheran ceremony in the Danish church in London) when she was born, & British because the UK had a
jus soli law (see below), i.e. birth here automatically made her British. I don't know if Danish law was the same back then, but I wouldn't be surprised.
British law did allow for dual nationality:
Any person who by reason of his having been born within His Majesty's dominions and allegiance or on board a British ship is a natural-born British subject, but who at his birth or during his minority became under the law of any foreign state a subject also of that state, and is still such a subject, may, if of full age and not under disability, make a declaration of alienage, and on making the declaration shall cease to be a British subject.
Pretty clear.
And since she was living in the UK, that's what counted.
Someone can be a dual national under the laws of one country, but not those of another, e.g. some countries (including the UK) require that renunciation of citizenship must be done before their own authorities, while others (e.g. the USA, Denmark) make it a condition of naturalisation to renounce foreign citizenships before their authorities. So if they only renounce their citizenship to the new country, the new country will consider them solely its own citizens, while the old country will consider them dual nationals.