The fact that the inflation target is a matter agreed between Minister and Governor has effectively protected the Bank from criticism by the government, and in the almost 14 years during which inflation targeting has been in place, the number of government ministers who have attacked the Bank can be counted on the fingers of one hand.
Given that the Minister of Finance is involved in agreeing the inflation target, it is not easy for him or other ministers to attack the Bank for having policy too tight unless inflation is, or looks likely to be, below the target.