Earlier quoted context omitted.
We do actually (»varetægtsfængslet« in Danish), but I forgot the appropriate term in English. I thought given the context that we were talking about bails, I didn't have to be specific.
Ah ok. I was confused by your question because while the distinction between pre-conviction "jail" and post-conviction "prison" is not always followed in English, "wrongful imprisonment" as a phrase almost always refers to wrongful conviction + imprisonment.
As example of what I'd think of as "unlawful imprisonment" there are problems in the UK with wives brought from countries where women, especially poor women, aren't treated very well - who are sometimes basically used as household slaves. The law against unlawful imprisonment doesn't require that they be chained up or in a locked room or anything, even a strong psychological coercion to remain ("You are my wife! You mustn't leave the home without my express permission") could be enough to make this unlawful.
Or you'll sometimes get people taking the law into their own hands, somebody catches a shoplifter and decides to put him in the walk-in fridge to "teach him a lesson" - that sort of thing. Again, that's a crime.