Best TV on today: New Year's Day 2017

Yet The Six Thatchers (writer Mark Gatiss’s take on The Adventure of the Six Napoleons) starts in the most playful, even carefree way. Sherlock (Benedict Cumberbatch) is as high as a kite after his bender on the plane at the end of the last series.

He’s even taken to tweeting and is as intellectually restless as we have ever known him. Meanwhile, his affable chronicler John Watson and wife Mary (Martin Freeman and Amanda Abbington) are rooted in happy domesticity as new parents.

But the clouds are gathering as the tight little group is drawn into the mystery of why someone is smashing busts of Margaret Thatcher. Everyone rises to the demands of a gripping, brutal story that leaves Sherlock (and Cumberbatch is at his finest and most mature) lost in the abyss. Gripping.

Mrs Brown's Boys, 10pm, BBC1

Mammy is brought home in a state of confusion by two gardai. Mark installs a stairlift for Grandad, who is out of hospital and prescribed marijuana. Betty worries that Bono is being bullied at school. Cathy is dating an obnoxious Frenchman. Rory and Dino are using a third party to communicate. And various other regulars are dolled up as the Flintstones. A typical day then in Agnes Brown’s household — and another busy episode with so much randomly thrown into the mix that the misfires outnumber the hits.

I find Rory and Dino’s mincing and mewing utterly excruciating, but Agnes’s tumbles and pratfalls always amuse. Here Brendan O’Carroll gets good mileage out of some spliffs, chocolate brownies and a smoking bra. And woe betide the charmless Gaston who bosses Cathy around, disses the Brown clan and says to Mammy’s face: “Zis woman is lower class than an olive farmer’s concubine.” Ouch!

EastEnders, 7pm, BBC1

It’s never a good idea to get married on New Year’s Day in EastEnders. Ronnie and Charlie? Bride ends up in a car crash. Barry and Janine? Groom is pushed off a cliff. Mick and Linda? Groom fights his bride’s rapist in a lake. Ian and Mel? Bride dumps groom by midnight.

So, what in the name of sanity are Jack and Ronnie thinking getting spliced on the most cursed day in the Walford calendar? And since we know that both Ronnie and her sister Roxy are on their way out of Albert Square, perhaps we should infer that it’s all going to end very badly indeed?

Dragons' Den, 8pm, BBC2

Like a long-running soap opera, Dragons’ Den has long phases – years when it’s not quite so good and years when it’s on fire. At the moment, it’s on the money, delivering plenty of those flashes of human drama as the funding assault course exposes character – or lack of it.

In some cases what is revealed isn’t pretty: “You worked for three merchant banks? God help us!” Nick Jenkins wails tonight at one hopeful, who took the unlikely route from male model to financier.

And there’s one of those awful moments when a Dragon bluntly demonstrates in a few seconds that a product just physically doesn’t work. But don’t worry: as usual, there’s a happy ending, with the kind of genius product idea that has you scurrying to find it on Google.

Still Open All Hours, 8pm, BBC1

In his eternal effort to lure the ladies, shopkeeper Granville (David Jason) buys a strange device on mail order (I don’t think the internet exists in the ageless, timeless Still Open universe). Every time he feels attracted to a woman, he gets an electrical charge, with unfortunate consequences.

The 1980s, 1990s, 2000s might well never have happened as Roy Clarke’s comfy sitcom still derives its fun from ill-fitting “undies”, henpecked men and old-boiler women who don’t stand any nonsense. The magnificent Black Widow (Stephanie Cole) has a new boyfriend, but there’s no funny business. Her swain is “entitled to only very limited pleasure in the early stages of our relationship”.

Diversity Presents Steal the Show, 7pm, ITV

With member Jordan Banjo fresh from the I’m a Celeb jungle, 2009 Britain’s Got Talent winners Diversity are kicking off the New Year with this one-off light entertainment special.

Welcoming guests like The Vamps and the cast of Motown: the Musical, the dance troupe will show off some new routines, inspire some amateur office dance-offs around the country and even get members of the public involved in their showstopping finale.

And of course it’s all good telly warm-up for group leader and choreographer Ashley Banjo, who’s set to join ITV’s Strictly rival Dance Dance Dance as a judge. Expect to see much more of these boys in the future.

Titanic: the New Evidence, 8pm, C4

Is new evidence on the Titanic still coming to light after a century? Irish investigative journalist Senan Molony believes so. He presents this doc, which promises to explore an overlooked aspect of the Titanic disaster – the fire on board when the ship set sail.

Using a new graphic technique to analyse recently unearthed photographs of the ship’s 1912 launch and maiden voyage, he spots an intriguing clue: a dark mark on the hull that was the result of a fire burning in the bowels of the ship.

The owners knew about the fire before the ship left port but kept it secret from passengers. Molony argues the fire was responsible for the decision to steam through the ice field at top speed.

Morecambe and Wise's Funniest Moments, 8:30pm, ITV

Adored song-and-gag men Eric and Ern are as much a part of the season as the Hootenanny, but what can we expect from tonight's compilation? Well of course, there's the time the boys were out-funnied by Beatle-fringed conductor André Previn. That has to be there. And with Glenda Jackson among the other celebrity contributors, presumably they'll have Eric's snooping Sphinx in the Anthony and Cleopatra spoof. Plus Angela Rippon's roving reporter with a difference. All the right sketches, then, but not necessarily in the right order.

Thailand: Earth's Tropical Paradise, 9pm, BBC2

In Pak Phanang, south-west Thailand, thousands of loudspeakers tweet birdsong to attract swiftlets to nest in specially adapted buildings. When the birds are done, the locals collect their edible nests to make into soup. This man-made situation is safer for the birds and less dangerous for the nest-collectors. Dolphins lead fishermen to the best fishing areas and are rewarded with some of the catch.

These are two examples of the almost spiritual connection between humans and nature in this beautiful country. Conversely hermit crabs are forced to make homes in discarded tin cans as a result of souvenir-hunting tourists emptying the beaches of shells.