Any former MPs who fear being out of work come early July should steer clear of The Traitors US (BBC3, Wednesday). Therein lies a cautionary tale about life on the outside of the Palace of Westminster. It’s chilly out there, people.

Forget the stuff about treachery and loyalty and all that beeswax, who is that little fellow lurking among the raggle-taggle bunch of US reality TV “stars” making up the contestants in this game show? Why it is none other than John Bercow, former speaker of the House of Commons.

“I thought you were the host when we first got here,” said fellow contestant Johnny Bananas from The Challenge reality show. Being the holder of an office dating back to the 13th century doesn’t impress this lot much.

Once he had put Mr Bananas straight about what a speaker does, the plucky Brit gave the assorted Real Housewives and Survivor cast-offs his party piece - a bellow of “Order!”. Just like old times.

I’m not saying it is a good or bad thing that the ex-MP should be on the show. Needs must when it comes to paying the mortgage. But ask yourself this, John: would Betty Boothroyd have done The Traitors US? Let that true star be your guide in post-Commons life and you won’t go far wrong.

So far, the actual host, Alan Cumming, has been too busy rolling his “rs” and being fabulous to bother much with Mr Bercow but I do hope that will change.

The woman who fell 4000 feet to a field after her parachute failed has to be up there in the top ten of true survivor stories. The Fall: Skydive Murder Plot (Channel 4, Tuesday-Thursday) related what happened on the fateful day, and tried to do so much more besides.

Skydiving was Victoria Cilliers's “thing”, her switch off from work and the pressures of a busy family life. She knew the drill inside and out, so when her parachute failed she went to the reserve, but that did not work either. The outcome seemed a foregone conclusion, yet Cilliers survived. What had happened?

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Shown over three nights, The Fall mixed documentary and drama to a degree I’ve only ever seen in the artier reaches of cinema. At one point, for example, the real detectives looked on, Greek chorus-style, as the actors playing them questioned the suspect (also played an actor). Tricksy Not half. Irritating? Wildly so. The story was shocking enough not to need any bells and whistles.

But after a while the method behind the narrative mayhem started to make sense. If the makers were trying to convey what it is like to juggle so many competing versions of the truth, they succeeded. The style won’t be to everyone’s liking, and it could go badly awry in the wrong hands, but different.

Big names migrating to the small screen is old news, but even by current standards Presumed Innocent (Apple TV+) has serious TV muscle behind it. Produced by JJ Abrams (Lost), adapted for TV by David E Kelley (LA Law) from the novel by Scott Turow, it’s a slick-looking beast and then some.

Jake Gyllenhaal stars as Rusty Sabich, a charismatic lawyer in the Chicago Prosecuting Attorney’s office who finds himself with questions to answer when a colleague is killed. Is he an innocent victim of office and Chicago politics, or is there a side to Rusty that’s at odds with his golden boy appearance?

The eight, hour-long episodes race along with plenty of hand brake turns and cliffhanger endings. Enjoyable as it is in A Few Good Men, shouty legal drama way, that is still eight hours of your life when two-hour movie would have done. Something, say, along the lines of the 1990 thriller with Harrison Ford? Sacrilege to say, but there we are.

More importantly, I was seriously unimpressed by the number of times the story flashed back to images of the bound and battered woman victim, and the dated treatment of female characters in general. Check the calendar, chaps: the 1980s are long gone.

Alastair Campbell Alastair Campbell (Image: free)

The Rest is Politics: election special (Channel 4, Tuesday) brought the popular podcast to terrestrial telly. This was the third outing for Alastair Campbell and Rory Stewart, plenty of time to get things right, so why did it look so wrong?

Watching two blokes banging their gums on a gloomy, no-frills set was just as tedious as it sounds. I don’t think I’ve ever welcomed an ad break so much, just for a change of scene.

Stewart reading out his scripted links added nothing to the liveliness of the piece. Campbell was vastly more at ease and better company, as long as you didn’t mind the name-dropping (“I was talking to Tony Blair the other day…”). But this was just a radio show filmed; fine for a clip on the TV news, but close to an hour of this at 11pm was a snooze.