Here is an imperfect abstract of the will Raffe Morley of Thursley, Surrey, dated 1582:

January 1581/2
Raffe Morley of the parish of Thursley in the county of Surr husbandman

To son Henry Morley: RM's freehold land in Thursley upon reaching age of 21. Until then, to be occupied by 
RM's wife Thomazin.

To RM's wife Thomazin: the lease of the copyhold land at [?North Thapple] (seems to either be rented from 
Robert Aylewon [or Aylwin?], or held in trust for him); if RM's wife will not perform this duty then RM's 
brother (-in-law?) John Bellchamber(?) is to do it and have the lease

To Robert Aylewon (Aylwin?), Agnes and Pole(?) (Paul?) Aylewon: (something) bequeathed to them by their 
father's will, once they come of age

To RM's children Henry, Richard and Margaret: lambes or landes

Legacies to every of RM's godchildren

Residue to RM's wife Thomazin.

Sole executrix: RM's wife Thomazin.

Executors: John Morley & John Bellchamber(?)

RM had a few debts. One was to Jo[hn] Morlee of guildford

RM was owed a few debts. One was from a Wm. M(a|o)(r|s)(b|l)e (slight chance this is 'Morley') of 
grashott (Grayshott). Another was from Richard Morley.

Reference for will:

London Metropolitan Archives and Guildhall Library Manuscripts Section, Clerkenwell, London, England; Reference Number: DW/PA/5/1582 (via Ancestry.com. London, England, Wills and Probate, 1507-1858 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.)

Thursley is not far from Haslemere, so a connection with the Haslemere Morleys below is plausible. Grayshott is even closer.

Ancestry also has a 1664 will for Roger Morley of Godalming in the same collection. It mentions some relatives in Guildford. His son John is the only other male Morley mentioned.

Henry son of Raffe may coincide with:

Henry Morley
+ --
	Mary, bapt. 16 August 1613 Thursley St Michael and bur. there 1 June 1615 [FreeReg TR]
	Joane, bapt. 1616 Thursley St Michael [FreeReg TR]
	Susan, bapt. 21 March 1618/19 Thursley St Michael [FreeReg TR]
	
Henry Morley
+ --
	Henry, bur. 1639 Thursley St Michael [FreeReg TR]
	
Henry Morley, bur. 1643/4 Thursley St Michael [FreeReg TR]
+ Katherine --, bur. 29 March 1644 Thursley St Michael [FreeReg TR]

Per FreeReg, one "Alce" wife of William Morraley was buried 01 Mar 1599/00 at Haslemere St Bartholomew.

A descendant of the Haslemere Morleys notes that the English literary scholar Henry Morley was a member of this family, and that a genealogical sketch is given in the first chapter of his biography by Henry Shaen Solly (published 1898). Here is a summary:

William Morley, surveyor; first Morley of this line spotted in Haslemere; also connected to Singleton, Sussex
+ Ann --
    William, glover and britches maker; parish clerk; bapt. 1690 Haslemere; bur. Haslemere 1749 [WikiTree 
         entry lists further descendants]
    + (1710 Rogate) Mary Urry of East Harding
        William [eldest son]
        [five other children older than Robert]
        Robert, of Haslemere, Stoke Aubernon and Farnham; also spent time at Molland House, Hants; b. 1720 
               Haslemere; d. 1807; bur. Farnham
        + (1747) Ann Kemp
            Robert, b. 1748; d. 1807
            + --
                Anne
                + -- Kendall, d. bef. 1838
            William, b. 1754 Stoke Aubernon; d. 1810
            + (1788) Alice Abbott
                Henry, b. 1793 Lichfield; d. 1877
                + --
                    Henry, b. 1822
        [two children younger than Robert]

Singleton is 2/3 of the way between Haslemere and Chichester.

The pedigree above has not been fact-checked.

The author of Henry Morley's biography suspected a connection to the Morleys of Halnaker, Sussex -- although he admits that there is no solid evidence, only the family tradition of a descent "from a brother of Sir William Morley who is buried in Boxgrove Church near Chichester". This biography mentions that Anne Kendall (see above) was paid money in exchange for renouncing a claim on the Halnaker estates. The details  of this claim were not known to the biographer, although he speculates that she could be the senior surviving heir of the surveyor William Morley.

The Morleys of Halnaker in turn claimed descent from the baronial family from Norfolk. Again, this is plausible but lacks proof.

Working against this theory is the existence of places called Marley Wood and Marley Common just south of Haslemere. Did the Haslemere Morleys take their name from this place? Or perhaps this place was named after the family. Further investigation into the history of Marley Wood is needed -- when was the name first recorded?

The Henry Morley biography also implies that the Haslemere Morleys may have taken their name from a place in Shermanbury, Sussex. But there are no known references to this place prior to the 1600s. More plausible is that the intended reference is Morley near Woodmancote, and it is there that the Morleys from Cowfold, Sussex may have originated.

So there are three competing theories as to the origins of the Haslemere Morleys:

1. Marley Wood and Marley Common, Sussex (near Haslemere, Surrey)
2. A cadet branch of the Morleys of Halnaker (originally from Suffolk)
3. From near Woodmancote, Sussex and related to the Morleys from Cowfold, Sussex

All three theories warrent further investigation. It would be nice to have a Y-DNA result for the Haslemere Morleys so that it can be compared against other Sussex and Norfolk Morley families. As mentioned above, there are British representatives. There are also Australian representatives.

Update: A member of this lineage has done Y-DNA testing. The result allows us to rule out the third theory.