William Broket had been a clerk in the Exchequer with good contacts. He served at least 3 justices —his 'Maisters' John Martyn, John Cottesmore, and William Paston—who advised him on a matter in the case brought by Danvers. The Master of the Rolls, Gerard de la Hay, had also arranged for him to gain access to the records in the Tower. The Master of the Rolls at that time was the guardian of all charters, patents, etc, entered upon parchment rolls, and the adviser and most important assistant to the Lord Chancellor in the old Court of Chancery (Macmillan Encyclopedia). To have had this man's help William must have had some influence. William was also clearly well educated—to have been a clerk he would have been in minor orders—and he used his own seal for letters.

William in all likelihood was the son of Thomas Broket, the current Treasurer's Remembrancer:

A position on the staff of the Exchequer for a son of the Remembrancer would have been natural in those days.
Someone with the same rare surname would almost definitely be related.
Gerard de la Hay, gentilman, came from Spaldington, Yorkshire, only c 15 miles from Bolton Percy. He acted as mainpernors with the same men from York as Thomas Broket: John Aglyon in 1422, John Cerf in 1426 and John Aglyon and John Holme in 1430 (Letters Patent 1422-30, pp 20, 171, 301).
At the time of the Danvers case William probably would have been 25-35 years old, and so born 1398-1408. Thomas had married Dionisia by 1393 and their eldest surviving son Thomas was b c 1396. William would then have been older than Edward, who was not born before 1417.
Harley 807 recorded a son William.
Two years previously it was most likely William who was granted property in York by the Treasurer. This was while Thomas was Treasurer's Remembrancer.