Not The Sopranos, not The Wire. Forget Broadchurch, Brideshead and even the sainted Coronation Street. The greatest  television series of all time is, in my view, Columbo.

The cop show about the Los Angeles homicide detective whom the TV listings persist in calling a “rumpled lieutenant” ran between 1968 and 2003 for 69 feature-length episodes. This  longevity and his incredible performance in the title role has meant that Peter Falk, who died four years ago, embodied his character like no actor before or since.

Imagine if William Hartnell continued in Doctor Who from its debut in 1963 and had only just retired now. Columbo even has his own TARDIS: a grey Peugeot convertible, mankier on the inside, which starts off dented and wheezy and grows progressively worse as the years pass; his version of the sonic screwdriver is, of course, the ubiquitous cigar, contemp-lative puffs on which help him to solve many a murder.

I came late to Columbo. Of course, I had seen it. But to truly appreciate the show there’s no point watching the odd one. You have to commit to 20 before you really get it. The character was based, in part, on Porfiry Petrovich in Dostoevsky’s Crime And Punishment – seemingly avuncular, conversational and confiding but with a fierce hidden intelligence and sharp moral sense. The fun is watching Columbo act dumb so that the crooks – a cravated parade of wealthy, snobby brainiacs – underestimate him.

There is a DVD box-set housed in a replica cigar case but the most enjoyable way to appreciate Columbo is to series-record a stack of episodes – this won’t take long, it’s on ITV and Channel 5 all the time – and then watch them, randomly, choosing whatever title takes your fancy.

Thus, you may find yourself settling down to an episode from 1975 in which Columbo takes on a murderous CIA operative (played by Patrick McGoohan) followed by an episode from 1998 in which Columbo takes on a murderous undertaker (played by Patrick McGoohan). Columbo’s hair will have grown a little less wild and rather more silver, his face bloodhoundish, but the plots will be the same delightful hokum.

The real pleasure, though, comes from watching Falk’s performance deepen with the decades. The characterisation is based on repetition and formula – the same physical and verbal tics, “Just one more thing” and all that – but as the years pass, he brings to the part a twinkle-eyed wisdom, with a mere hint of despairing impatience, on the subject of human folly and frailty.

The last ever episode, Columbo Likes The Nightlife, is on one level a poor finale: a piece of nonsense set in LA clubland, in which – spoiler alert! – the victim’s body is hidden beneath a fishtank set into the dancefloor. Yet this is Falk’s Lear. He is world-weary, a man out of time, deeply serious in his pursuit of evil even with a pink feather boa draped round his famous beige raincoat.

Just one more thing? Let’s not be greedy. After 35 years, Columbo gave us plenty.