What’s currently the top-rated drama on British telly? It’s not Broadchurch, and it certainly isn’t Wolf Hall. Call the Midwife takes that crown – but chasing at its heels is the show nobody’s talking about: BBC1’s sun-dappled homicide caper Death in Paradise. Four series in and Britain refuses to give up on what seems like an unremarkable show. But being unremarkable is its secret.

The appeal of Death in Paradise is so maddeningly straightforward that would-be crime drama writers must be elaborately murdering themselves with frustration. It’s an undemanding detective show, with nice Caribbean scenery. That really is it. Check the forums, and commenter after commenter simply says it’s pleasant to watch a programme set in an exotic location when it’s dark and cold outside.

I’ve met TV schedulers. They’re tetchy, haunted creatures, wizened from endless days hunched over giant spreadsheets, failing to please everyone. They deserve a no-brainer now and again. Placing Death in Paradise in January, to cheer up seasonally sad viewers who can’t afford to fly off for winter sun, is just that. ITV’s put the last couple of series of Benidorm on in the pits of the January doldrums, too.

Exotic locations and old-school sleuthing ... Death in Paradise. Photograph: BBC/Red Planet Pictures/Mark Harrison

Death in Paradise continues to smash it, ratings-wise (about 8.5 million people watch it every Thursday), even after making two fundamental changes that could have sunk a more vulnerable show. Originally, the English detective solving crimes on the fictional island of Saint Marie was Ben Miller as Richard Poole, who rigidly kept his suit and tie on at all times, and was volubly dismayed at working in such a lackadaisical backwater. Miller had a bit of antisocial rage about him; squint and you might have been watching John Cleese.

Miller tired of filming so far from home and was replaced last year by Kris Marshall as Humphrey Goodman, who … well, he’s archetypal Kris Marshall, an impotent, frowning manchild. Goodman favours loud shirts and crumpled linen, and enjoys life on Saint Marie, so that was the end of the angry-fish-out-of-water conceit. In came romance, in the form of a will-they-won’t-they between him and local policewoman Camille, played by popular original cast member Sara Martins.

Now that’s gone, too; Martins departed three weeks ago, bequeathing her tolerant-sidekick role and boyish short shorts to French actor Josephine Jobert. So the broom’s got a new brush and handle, but so far the figures aren’t dipping.

Fans probably won’t mind losing the tiny bit of grit that used to be in the oyster - DIP is all about taking it easy. It’s almost a parody of detective drama cliches, with old favourites, such as locked-room killings, decoy confessions, and denouements where the sleuth gathers everyone together in a room before revealing their secrets, all jovially recycled. Suspects are interviewed and eliminated one by one. Evidence is slowly recapped. It’s often reassuringly easy to guess who the murderer is.

These are bloodless, solidly middle-class mysteries – no gore, no social issues and none of your outlandish Midsomer Murders poisonings and impalements here, thank you. In any case, MM goes on for two hours, which is a bit too much of a commitment. DIP wraps up in 60 breezy minutes, and there’s plenty of time to look at the beach along the way.

It’s like dreamily flipping through a holiday brochure. As long as they don’t suddenly relocate it to Portsmouth, Death in Paradise can enjoy a few more years in the sun.