One thing that a lot of old British detective shows have in common is a protagonist that is lacking something significant. In fact usually for one reason or another they're very much alone. Frost has been living with a woman who didn't love him. Tennison has never really found a home for herself either at work or with a man that lasted. Gently is so buttoned up that he won't share anything about his inner life--which means we have the sense of him as isolated not only from others but from us. Morse spends pretty much every episode hitting on women and wanting his partner Lewis to come have a beer with him. And when Lewis gets his own show, he's lost his wife. He's actually a lot more open and friendly than the others, but the struggle is there. (Also, his partner struggles deeply with connecting with people.)
Each of these shows deals with that emptiness in their life in different ways. GENTLY is really a procedural that very very slowly over years lets us into the interior life of Gently. MORSE on the other hand is in some ways barely a procedural at all. Yes, we go through the motions, but more than anything it's a show about Morse. And PRIME SUSPECT really does the work of both--it's deeply procedural, but it is very very much about Tennison's personal experience in the case, too.
But the point is, what makes them all compelling is the fact that their characters have that hole, that gap inside that they are desperate to fill and can't.
I find it a great question to consider when writing a script: What is my character missing? What is the hole that they are desperate to fill? It doesn't have to be rocket science--I don't think it's a coincidence that for most of these characters the issue has something about loneliness and relationship. But one thing that's clear watching these shows: once you know what that hole is, it really gives your character direction and momentum.
