I note that the published genealogy you reference states that William PERYE was of Water in Membury. Oldest surviving registers for Membury date back to only 1637 with Bishop's transcripts going back to 1620. Parish registers in general only began in 1538 so prior to that time you will need to consult Manorial Rolls, Chancery documents and the like. I would suggest you start with the National Archives
http://discovery.nationalarchives.gov.uk/ - enter PERYE in the search engine and then refine the results by date. You may also find this useful: Membury, Devon
Historical Description
Membury, a village and a parish in Devonshire. The village stands near the river Yarty, and near the boundary with Dorsetshire, 3 ½ miles N by W of Axminster station on the L. & S.W.R., with a post office under Axminster; money order and telegraph office, Axminster. Acreage of the civil parish, 4394; population, 645; of the ecclesiastical, 3759. The manor belonged to the Courtenays, passed to the Drakes, and now belongs to the Ecclesiastical Commissioners. Yarty, now a farmhouse, was the seat of the Yarty family ;
Waterhouse, anciently called Waters, was the seat of the De la Water family. Membury Castle is a well-preserved ancient British camp of about 2 acres on a hill. The living is a perpetual curacy, annexed to the vicarages of Axminster and Kilmington, in the diocese of Exeter; joint value, £600 with residence. The church is partly Early English, partly Decorated, has been restored, comprises nave, transept, and chancel, and contains a fine monument to Sir S. Calmady.