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Here's a link to a Wikipedia page on the police ranks in the UK:
http://en.wikipedia.org/wiki/Uk_police_ranks
It's hard to say what the direct American equivalents would be to the UK ranks because unlike their counterparts in the United Kingdom, which use a standardized set of ranks throughout the country, police departments in the US have wildly varying ranks and command structures.
The rank of Detective Chief Inspector is roughly equivalent to the rank of Captain in most US police departments insofar as both ranks are two steps above Sergeant. However, in the US, an officer who holds the same position that DCI Tennison does in Prime Suspect, the leader/commander of a squad of detectives, could be a senior Sergeant, Lieutenant or Captain depending on the rank structure of their department. It should also be noted that, in some police departments, "Detective" is a rank rather than a specific duty assignment.
I hope that helps.