Blackett was commissioner for militia in March 1660 and captain of foot militia in April 1660. From August 1660 to 1661 he was commissioner for assessment for Newcastle. He was elected sheriff of Newcastle for 1660 to 1661, when he was described as "a loyal man, much beloved and fit for the office". From 1661 until his death he was an alderman of Newcastle. He was governor of the Hostman's Company from 1662 to 1664 and was Mayor of Newcastle for 1666–67 during which year of office he appeased a riot over taxes with an assurance that payment was voluntary. He was governor of the Hostman's Company again from 1667 to 1669 and was a commissioner for assessment for Newcastle from 1667 until his death.