Since you have an R56 I doubt the tensioner is the problem. They seem somewhat more problematic on higher mileage R53 MINIs.
The R56 being direct injection tends to make a clicking sound. That's a guess on my part.
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Crashton Club Coordinator
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If it was the tensioner you'd hear what sounds like a diesel engine on a cold startup.
Most likely you hear the fuel injection. -
Could also be low oil. We burn through it pretty quick.
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I hear this electrical tick on every cold startup then goes away after a few minutes. You're dead on accurate on where you say the sound is coming from, I've even said it sounds like it's below the brake master cylinder/firewall area. I also sounds like an electronic solenoid or a coil spark, been hearing it for seven months with no ill effects.