In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Linchmere like this:
LINCHMERE, or LYNCHMERE, a parish in Midhurst district, Sussex; on the Midhurst and Haslemere railway, 3 miles SW of Haslemere. Post town, Haslemere, under Liphook. Acres, 2,101. Real property, £1,131. Pop., 283. Houses, 56. The property is chiefly divided among four. The manor belonged anciently to the De Percys; passed to the Fitzalans, - afterwards to Sir William Fitzwilliam; and belongs now to the Earl of Egmont. ...
Shulbrede priory, in this parish, was founded in the time of Henry III., by Sir Ralph de Arderne, for Augustinian canons; was given, at the dissolution, to Sir William Fitzwilliam; and has left some remains, on part of which are still discernible some curious fresco paintings. The living is a p. curacy in the diocese of Chichester. Value, £60. Patron, the Rev. W. H. Parson. The church is of the 14th century; was restored in 1856; and consists of nave, aisle, and chancel. There is a parochial school.
GB Historical GIS / University of Portsmouth, History of Linchmere, in Chichester and Sussex | Map and description, A Vision of Britain through Time.
Date accessed: 25th April 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Linchmere ".