Jane Tennison is in her last tired, limping laps as a copper in several ways in “Prime Suspect: The Final Act.”

On the simplest level, Tennison (Helen Mirren) is near 60, near retirement and near the end of life as she has known it. Are you retiring to Spain, a colleague asks. No, Florida, she says. It’s where coppers retire these days. Cops and Mafia.

She is also near the end of her rope.

As the four-hour “Masterpiece Theatre” drama opens, she awakens hung over, with bruises she can’t recall receiving. She has been in the London Metropolitan Police since she, in effect, ran away from home at 17. The question rises whether she will be able to muddle through this last especially painful case.

As faithful followers of “Prime Suspect” know, her struggle to rise to her current status, detective superintendent, made a climb up Mount Everest look like a gentle glide around a roller rink. Aside from the regular rigors of getting to be a good cop, one of her bosses, Bill Otley (Tom Bell), worked methodically for years to sabotage her career.

The case that Tennison knows will be her last involves a 14-year-old missing girl who, of course, turns up dead – and, it soon turns out, pregnant. Interviewees include teenagers whose attitudes range from prankish to hostile to other things – including possible guilt.

Of course, the case is never the only story in “Prime Suspect.” Tennison’s love life is in the loo, her staff knows she drinks, her boss knows she drinks, and one of her teenage interviewees knows she drinks. And her father is dying. Soon she is scheduling her investigation activities around hospital visits and Alcoholics Anonymous meetings.

And at her first AA meeting she finds herself looking at her old nemesis Otley.

One part of AA progress is to apologize to as many people as you can find, and Otley unburdens himself. Tennison naturally resists, but circumstances alter the case.

The murder case proceeds in reasonably orderly fashion until the end of the first half, when it suddenly becomes another case. Adults who seemed not so involved at first begin to look more interesting.

Then Tennison reflexively does something that gets someone killed. Soon after, her drinking problem threatens to graduate to a crisis.

Because Tennison is so advanced in the hierarchy, “Final Act” can’t hit the tension-from-the-top mode as hard as usual. Frank Bullitt, Harry Callahan, Sam McCloud and other police detectives often find themselves in bitter conflict with overlings, some of whom seem almost to be obstructing the procedures in the police procedurals. But Tennison’s issues with her actually sympathetic boss clearly are self-made problems.

Many a movie hero learns that no one – fighter pilot, cop, doctor, teacher, what have you – is an island, that one must finally reach out and allow others to reach in. Tennison never gets far with this lesson. The friendship account in the bank of her emotions is disastrously low on funds.

It is soon clear that a happy ending to this story and series is unlikely. As in Ross Macdonald’s novels, solving the crime can bring only misery to various characters. We are asked to worry that Tennison may do herself out of being in at the finish.

Most important, in deep but unconscious denial, Tennison has given no thought whatever to retirement. Her boss glumly observes to one of her concerned officers that a lot of old coppers just go home and drink themselves to death.

No one watches “Prime Suspect” for upbeat entertainment, and the faithful need not fear that some ray of sunshine will come beaming in from left field.

Since 1991 Helen Mirren has suffered through six multi-part episodes before “Final Act,” and she registers every minute of Tennison’s tough life in a tough job. A great deal of the film is simply Tennison reacting (stonily, usually) to something she has just heard, silently sifting for nuance and implication.

We may wish for Tennison to labor more, but Mirren turned 61 on July 26. Unlike Tennison, Mirren will not have to sit at home and drink herself to death unless she really wants to. She is quoted as having said, “All you have to do is to look like crap on film and everyone thinks you’re a brilliant actress. Actually, all you’ve done is look like crap.”

As Tennison, Mirren still looks like gold.