Robert’s forebears took their name from the hamlet of Grafton (six miles from Shrewsbury), where his father still held lands in 1386, but his immediate ancestors had established themselves as burgesses of Shrewsbury at the beginning of the 14th century.
In the meantime Grafton had taken some part in the government of Shrewsbury: in December 1380 he had replaced his father as one of the local collectors of the poll tax; the following March he was commissioned to see to the peaceful administration of the town following riots there, and in July 1384, on payment of an entry fine of £5, he was formally admitted as a burgess. He was frequently called upon to witness local conveyances. Following his second return to Parliament, the borough paid him 36s.7d. towards his expenses; and he shared with his fellow Member, Hugh Wigan, a further re-imbursement of £3 4s. In August 1389 he was elected as one of the council of 12, and about a year later as bailiff. Although he obtained further royal letters of exemption from office, he went on to serve as bailiff for one more term and was twice nominated to the body of assessors.