The comedy - penned by Charlie Brooker - stars Hannah as tortured DI Jack Cloth and Suranne Jones as his partner DC Anne Oldman.
"I'm pretty bored - probably more bored than most of the audience - with procedural cop shows," the Scottish actor told Digital Spy. "And doctor shows which are really cop shows, but they're talking about diseases rather than killers or bank robbers.
"It's all the same procedural dullness. [This series] is actually what needs to be done, so it was a no-brainer."
A Touch of Cloth creator Brooker added that it was always "very much" his intention to cast actors whom fans of UK crime drama might recognise.
"Part of the joke is that if you switched it on and just stumbled into it - and maybe the sound was off - you'd think you were watching the real deal," the writer explained.
"With John Hannah and Suranne Jones at the core, you've got two very credible actors who you would associate with blue-chip drama."
A Touch of Cloth debuts on Sky1 on Sunday, August 26 at 9pm. Two follow-up instalments have been ordered, with Doctor Who star Karen Gillan cast in the third edition.
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