Get Well Soon has a strong cast but very weak writing. The main weakness is the characters, none of whom are very likeable or funny.
It's possible it was made a decade or so too late: the "wartime sitcom" probably had its heyday in the 1960s and 1970s with Dad's Army and others, possibly to as late as the early nineties with Goodnight Sweetheart. But Goodnight Sweetheart combined the present with the past and had a more interesting and unique concept than Get Well Soon. The concept of long-term patients in a hospital also peaked in the 70s with Only When I Laugh and the Carry On films.
But even taking its setting aside, too many of the characters are odd and unpleasant and weird. Matthew Cottle is basically playing Martin from Game On (no surprise, the two series overlapped) which might have worked if he'd had the right kind of characters around him. But Eddie Marsan as a fellow patient is aggressive and horrible. Anita Dobson as the mother is very unsympathetic. Samantha Beckinsale as a recently widowed wife is just weird and unconvincing. There's an overly silly vicar and Robert Bathurst is completely wasted as a unfunny-mentally-deluded former flying ace (compare to Rik Mayall's "Ace Flashheart" in Blackadder Goes Forth). The "comedy camp" hospital porter is more like a caricature of a "comedy camp" character (as in Ricky Gervais's show-within-a-show When the Whistle Blows/Extras).
I have only watched the first episode of this, so it's possible the series improved. If I managed to see the others I'll give them a try and edit this review if so. But on the strength of this first episode, it's no surprise this "comedy" failed to make a second series.
