A Touch of Cloth has been co-written with Daniel Maier, a writer on ITV1's Harry Hill's TV Burp, and sets out to be a "spoof of every British crime drama made in the last decade".
Hannah stars as DCI Jack Cloth, a "maverick, heavy drinking loner" who throws himself into his work after the death of his wife.
He is teamed with a "plucky, no-nonsense sidekick" played by Jones investigating a series of grisly murders. Rhind-Tutt plays their boss, Tom Boss.
It is the latest scripted TV project for Guardian columnist Brooker, who has also written comic drama series Black Mirror for Channel 4, described as a hybrid of The Twilight Zone and Tales of the Unexpected. He previously wrote Big Brother-based zombie thriller Dead Set, for E4.
Brooker said: "After you've seen A Touch of Cloth you'll never be able to watch another detective show again. Not because it's a devastating piss take, but because you'll have smashed your TV into pieces in a disappointed fury."
A Touch of Cloth is part of Sky's commitment to up its investment in original British content by 50% over the next three years.
It follows recent new launches including sitcom Trollied and comedy drama Mount Pleasant, which began on Sky1 on Wednesday. Other Sky1 original productions include dramas Thorne and Mad Dogs, and the Bafta-winning Flying Monsters 3D.
The head of comedy at Sky entertainment, Lucy Lumsden, said the spoof was "witty, naughty and unashamedly silly".
A Touch of Cloth will be made by Zeppotron, the comedy and drama production arm of Big Brother producer Endemol UK.
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