Few television-related stories have been more welcome this autumn than the news that BBC4 has confirmed its aquisition of the wonderful Parks and Recreation.

Forget the Emmys showered on Modern Family: this Amy Poehler comedy, which centres around the oddball employees of the parks and recreation department in the fictional town of Pawnee, Indiana, is arguably the strongest sitcom on US television right now, making its late arrival in Britain all the more surprising.

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So what makes it so brilliant? As with many great shows, the key can be found in its evolution. Scripted by US Office writers Greg Daniels and Michael Schur, it was conceived as a vehicle for then Saturday Night Live star Amy Poehler and started out as a sort of companion piece to their earlier show, using a similar fly-on-the-wall mockumentary technique as it followed Poehler's Leslie Knope, a mid-level bureaucrat with delusions of grandeur, around her daily grind.

In truth, Parks & Rec's six-episode first season isn't that good. It took a while for the principal cast to get comfortable and the show seems to be laughing too much at Poehler's ambitious Leslie rather than with her. Yet stick with it, because those glitches were swiftly sorted out and the final episode of the first season sees the show find its feet.

That it did so is in large part because of Poehler, a naturally warm comedian who convinces you to root for the kind-hearted Leslie and her love of all things bureaucratic. Her fumbling towards success became portrayed less as Michael Scott-style buffoonery and more as the product of an admirably cheerful vision of the world. This is a woman who throws an annual Galentine's Day celebration on 13 February for all her female friends, who loves waffles and whipped cream immoderately and who has a celebrity crush, brilliantly, not on Barack Obama but on his wild card vice-president Joe Biden.

Whether marrying penguins, organising harvest festivals or running for office, Leslie's view of the world remains so ludicrous in its optimism that it's impossible not to root for her: you laugh at her errors but you still want her to succeed. She's that rare thing in an American sitcom, a female lead who actually has female friends and spends time having ordinary conversations with them. Her well-drawn relationship with best friend Ann (Rachida Jones making the most of what could be a thankless straight role) not only ensures that Parks & Rec routinely passes the Bechdel test (wherein two women meet and talk about something other than a man) but also provides us with a rare example of a believable on-air female friendship.

As Leslie's character stabilised, so the cast around her came into focus. We learned to love her libertarian yet luddite boss, the magnificently moustached Ron Swanson (a scene-stealing performance from Nick Offerman), a man whose only true weakness appears to be women named Tammy; were amused by her co-workers, the lecherous Tom (played with sly perfection by stand-up star Aziz Ansari) and the apathetic April (the wonderfully deadpan Aubrey Plaza) and won over by Leslie's offbeat romantic liaisons, played by a host of rising comedy stars from Louis CK's mild-mannered police officer to Adam Scott's serious, socially awkward Ben.

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Giving one of the best performances of all is Rob Lowe as Chris Traeger, probably the only person on earth as enthusiastic as Leslie. Lowe's relaxed turn is not only one of the highlights of his career it also demonstrates the show's real strength – its lightly worn charm.

For Parks & Rec is a genuinely warm-hearted comedy. It both likes and is interested in its characters and because of that – and also because they are well-drawn – we end up liking and being interested in them too.

Yes, it has some great jokes from prize-winning miniature horse Li'l Sebastian to any number of lovingly ridiculed small-town events and, yes, there's something brilliant about the way in which it tackles dry political minutiae with a light touch; civic bureaucracy appears almost sexy.

But ultimately, this is a show that works because of the kindness at its centre. You'd run a mile to avoid most sitcom characters; the Parks & Rec gang make you want to genuinely hang out with them as friends.