Robert may have been the son or nephew of that wealthy member of the potentiores, John Brunham, several times MP for Lynn between 1365 and 1384, six times mayor, alderman of the Holy Trinity guild and father of the famous mystic, Margery Kempe.
Brunham occasionally acted as trustee of properties in the vicinity of Lynn. In 1395 he was enfeoffed by William Doraunt, esquire, of lands in Setchey, South Lynn, Clench Warton and elsewhere; in 1401 by the Leicestershire knight, Sir Thomas Boyville, of the manor of Bealfus in South Creake; in 1414 of lands in Wormegay, Runcton and Middleton; and before 1417 by Edmund Beleyeter of his manor of ‘Feltham’s’ in Great Massingham.
In September 1407, during his first mayoralty, Brunham attested the parliamentary election indenture, and he acted similarly in May 1413 and November 1414. Meanwhile, in December 1411, as one of the potentiores, he had been bound over in £100 to obey the mayor, and was then appointed as one of the 18 arbitrators who, drawn from all the three parties which were in conflict, were authorized to settle the town’s constitutional disputes. He was automatically excluded from the committee of nine (composed only of inferiores and mediocres) which took over the administration of the borough the following May. When, as alderman of the guild, Brunham held the municipal elections on 29 Aug. 1419 he encountered opposition from members of the 27. He is reported as saying ‘Above all things peace is good for you’, to which an opponent, Geoffrey Bilney, replied, ‘we might have had peace and tranquillity in this town for a long time back if you had wished it, but you prevented it’.
