Alys' parentage needs sources to confirm. There seems to be some disagreements as to whether or not it is Thomas de Astley and Edith Constable. The wording in the inscription at the Church of St. John the Baptist (see in the notes section below) seems to indicate that they might have been more distant ancestors than parents.Langholf-2 21:58, 19 October 2013 (EDT)
Alys' will was proved 15 October 1538. She requested to be bured in the Church of St. John the Baptist before the Rood.
Alice Perkyns mentions: Jeyn Sleyter, "my daughter," Juliana Cumpton "my daughter," Henry Perkyns "my son," executor; John Stokys, Clerke, Thomas Gierke, Richd. Smyth, supervisors; John Brendon, Gierke, George Dobbe, Wiilm. Freinan, Thomas Dunkele, Richd. Bassett, witnesses.
The inventory, dated 10 Oct., 1538, was taken by: John Brendon, Clerke, Wm. Buttye, Wm. Freman, Thomas Dunkley, Edwd Twygare, appraisers.
Amount £36 2s. Id.
Proved at Lichfield, 15 October, 1538, by Henry Perkins. (Lichfield. Registry, Act Book No. 2)
In St. John the Baptist Church at Hillmorton Parish, in the side aisle, on the right facing the altar, are life sized effigies of Thomas and Edith de Astley who lived in the 14th century. According to the Vicar of St. John they are the forebears of Alice de Astley who is said to have married Thomas Perkins, whose will directed that he "be buried in the Church of St. John the Baptist before the Rood." An old inscription of the church (Church of St. John the Baptist before the Rood) states that "In the middle ile (sic) of this Church are two grave stones of marble, each of them having small portraitures in brass of a man and a woman, with divers children; on one of them is this Inscription: Here lyeth Thomas Perkins and Alice and Elizabeth, Our Lord save their souls from everlasting death. Amen." 
English Origin of Six Early Colonists by the Name of Perkins, Paula Perkins Mortensen, Higgins Book Company, Massachusetts, 1998, pgs 3-4
Notes on the Perkins Families in England, D. W. Perkins, compiler Publication: n.p., Salem, Mass, 1894
Alys is not the daughter of Thomas D'Asltey and Edith Constable:
Sir Thomas D' Astley who married Edith Constable died at the battle of Evesham in the 1265. He is not the father of the Alice who married Thomas Perkins in Hillmorton. The D'Astley family left Hillmorton when one of the sons married an heiress in Norfolk. They still owned it but the family seat was in Norfolk.