Guidelines issued by the Association of Chief Police Officers suggests that a fixed penalty for speeding should not be applied unless the speed is 10% + 2mph above the speed limit. For a 30mph zone this is 35mph.
This is so as to avoid arguments about instrument calibration and so on.
Generally prosecutors do not have access to tachograph information when dealing with speeding offences, nor should they need it. They usually have ample evidence to support their allegation.
It is most unlikely that your friend has been accused of speeding at just 1mph above the limit.