You can have dual (or multiple) citizenship, permitting you to lawfully hold several passports.
Lots of people, for example, hold both British and Irish citizenship. Look at the flow chart I've linked to. That will show whether you're entitled to Danish citizenship (and hence to a Danish passport). If so, you could have had a Danish passport from birth (as well as a British one).
The Spanish Embassy in London can advise you about your possible eligibility for Spanish citizenship:
[email protected]
Chris