Jenyns died before the work was finished, and Stow reported that John Kerkbie, John Garlande and Nicholas Leveson contributed to its completion in 1532. Sir William FitzWilliam was also substantially involved. St Andrew Undershaft is one of the very few medieval churches to have survived in the present-day City of London. Jenyns made his will on 29 January 1521/2, appointing John Nechylls and John Kirton his executors and John Baker overseer. He was to be buried in the conventual church of the London Greyfriars. He desired them to arrange that 24 poor men's children 'such as can say our lady matens or the psalme of Deprofundis' should bear torches at his funeral, and that the five orders of Friars, the priests of the Fraternities and of St Augustine Papey, and the 60 priests and company of the Fraternity of Parish Clerks of London should accompany his funeral procession. He provided for many masses of requiem and dirige, for his soul and for the souls of his wives, to be sung by the priors and convents of Elsing Spital (St. Mary within Cripplegate), of St Mary Spital without Bishopsgate and of the London Charterhouse, the Abbots of Faversham, Boxley and Stratford, the Franciscan friars at Greenwich and Richmond, and the two Lazar houses; and there were plenty of charitable bequests to be made. This will was proved on 28 May 1523. In June 1522 he made a separate will to John Bennett, granting three parcels of land or property in London, and provision for the payment for his obits, to the Merchant Taylors. Bennett fulfilled his intention in 1527: this was a means of assuring the Guild's future title to the property. Obits were still being kept for him by the Merchant Taylors at St. Martin Outwich during the 1540s, but the moneys reserved for that purpose at the Greyfriars were surrendered to be stripped of their superstitious uses (and given over to profane ones). Jenyns had a tomb prepared for himself in the 'Postles Chapel on the south side of the choir of the church. His monument is illustrated in polychrome in the "Book of Funerals" of Sir Thomas Wriothesley, Garter King of Arms (died 1534). In this Herald's image the long sides of the rectangular tomb-chest are shown each divided into three equal panels framed by slender squared pilaster strips with gothic detailing.