Bramshott’s antecedents had long been well-established among the gentry of Sussex and Hampshire. On his mother’s side he was a great-grandson of John, Lord Bohun of Midhurst (d.1367), and it was through her that he inherited the substantial Lisle estates which included three manors on the Isle of Wight as well as Lordington and Compton in Sussex. Claims of other members of the Lisle family to certain of these properties had been for the most part successfully refuted by his parents.
Both of Bramshott’s terms as sheriff and all of his service on royal commissions of array took place in Hampshire, yet it was the neighbouring county which he represented in Parliament. There, to the local standing provided by his own property was added the newly-acquired benefit of his relationship to Pelham, whose landed resources in Sussex rivalled those of the earl of Arundel. Bramshott probably died not long after he and his wife made a settlement on their younger son, Baldwin, of the manor of Gatcombe and land at Hilsea, at Michaelmas 1432. Certainly, he is not recorded among the gentry who in 1434 took the oath against maintenance, although his elder son, John, appeared on the lists for both Sussex and Hampshire. Nor was he mentioned five years later in the will of his widowed sister, Joan Pelham, whose residuary legatee was his son John. Bramshott’s widow lived to see John’s marriage in 1444 to Sir John Pelham’s grand daughter.