The life of Chloe Sevigny’s Mia is reshaped when the hired killer becomes the legal guardian of several kids on DirecTV’s “Hit & Miss.” (DIRECTV)

Helmet lamps on, gang, as we go TV spelunking once more. I’m about to give a good review to a TV show called “Hit & Miss” that is rather dark, very British (lost half of you right there), and about a transgender woman who is also a hired killer, and stars the enduringly weird Chloe Sevigny, who has spent her career pursuing roles in projects that are almost always fringy. To top it all off, this show is available only to DirecTV subscribers, who will be asked to locate it among a morass of channel offerings. (The pilot episode was briefly available online to everyone.)

Including the false penis Sevigny wears for her full-frontal nude scenes, could we get any more niche? I’m guessing not.

But that’s the reality in which many of us now hunt for good television, vaguely aware of worthwhile shows that are so far off the dial that . . . well, what’s a dial? In spite of this barrier to entry, I urge you to have a look (somehow) at “Hit & Miss.” DirecTV’s exclusive American airing of the six-part drama begins Wednesday night.

Sevigny plays Mia, a loner who works as a brutally efficient hit-person, taking her assignments from a criminal underworld heavy (Peter Wright) who pays her in stacks of cash. Mia’s the perfect killer, since she’s all but erased her previous gender identity as a man, as she works toward becoming the woman she was meant to be with the help of hormones and surgeries. (That cash she’s earning is being saved up for the final operation, below decks.)

Mia belatedly receives a letter from a past love, Wendy, who reveals that Mia fathered a son, Ryan (Jorden Bennie), when they lived together. Now dying of cancer, Wendy has named Mia the legal guardian of not only the 11-year-old boy but also of Wendy’s other children, fathered by other men, who range in age from 6 to 16.

By the time Mia drives out to the bleak Yorkshire countryside to check on the family, Wendy has died and the older children resent the arrival of a stranger who has been entrusted with their care. In the most remote way, “Hit & Miss” is a sort of “Sound of Music” story without any smiles. How do you solve a problem like Mia, who lives only to kill? Appeal to her motherly (and fatherly) instincts. Instead of teaching these neglected imps to sing, she teaches them how to stick up for themselves against their bully landlord. She also keeps her night job, bumping off a list of losers who’ve run afoul of the mob.

I realize this plot sounds laughably bizarre, but “Hit & Miss” has a strikingly strong sense of pace and character. Sevigny, who played the craziest wife in HBO’s polygamy epic, “Big Love,” has found a nearly perfect part here as Mia becomes a thoroughly engaging and deeply conflicted character. The role is written (by Sean Conway) with a surprising sensitivity that is heads above the cheap “tranny” jokes we usually get from a popular culture that fails again and again to discern cross-dressing antics from gender-identity issues.

“Hit & Miss” was created by Paul Abbott, whose credits include the original British version of “Shameless.” Both shows have a similarly blunt sense of humor, although “Hit & Miss” has many more depressing shades of blue. It’s a beautifully sad — and beautifully imagined — downer.

Hit & Miss

(one hour) premieres Wednesday at 10 p.m. on DirectTV’s The Audience network.