Whether something is asked in a form of a question or stated in the form of an announcement has a big difference to the psychology of the situation. You should have a look at Neuro-Linguistic Programming. While this isn't NLP exactly, it's kinda close.
Coppers invariably begin fishing encounters with small-talk; as if they're being friendly and courteous. They'll never be explicit about you being detained or otherwise. On the surface, I suppose they are being courteous; except, since I view them as professional predators, I'm aware they invariably have an ulterior motive. A general member of the public, if they have need to stop someone to ask something, will usually express an apologetic tone for their intrusiveness, and thank profusely for your help, even if you couldn't help. Whenever did you encounter such a tone with an LEO? I'm betting never.
In the instance you relate, the coppers started telling you they were looking for a suspicious person; which is small-talk. You could simply say, "sorry, I don't know that person, I cannot help you." and "Have a good day sirs!". On you go. They never were explicitly detaining you (according to your account), so you should, IMHO, presume they're not. Of course, if they become agitated and edgy, you can always wind back the indifferent assertiveness and go with their flow.
The political class and their praetorian sycophants have way too much power, simply because power is there for the taking.