What's In A Name:

Most people in England did not have anything approaching an hereditary surname until the end of the 14th century. The growing need for identification in mediaeval England had probably led the clerks to give people these additional names. They might be those of their fathers (patronymics) or of some other relation, or the name of the place where they lived or from which they had come (locative surnames), or the names of their offices or occupations, or some descriptive or nick-name.  

See also the Barnes Family Coat of Arms.

Barnes

The Oxford Name Companion::

1. English: topographical name or occupational name for someone who lived or worked at a barn, from the genitive case or place of Middle English barn, granary (from the Old English bere; barley + ćrn house). The place name Barnes (on the Surrey bank of the Thames in West London) has the same origin and some bearers may be members of families hailing from there.
2. English: name borne by the son or servant of a barne, a term used in the early Middle Ages for a member of the upper classes, although the precise meaning is not clear (it derives from the Old English beorn / Old Norse barn - young warrior. Barne was also occasionally used as a given name (from Old English / Old Norse byname) and some examples of the surname may derive from this use.
3. Irish: Anglicised form of the Gaelic Ó Bearáin - descendant of Bearán, a bymane meaning 'spear'.
4. Jewish: probably a variation of Parnes.

Variations of 1 and 2; Barne and Barns
Variation of 3: Barrington
Variation of 4: Barness

Barnes

Surnames of the United Kingdom by Henry Harrison 1912::

1 pl. (local) and genitive. (person) of Barn(e), q.v. Barnes in Surrey occurs as Barne in the Domesday Book.
"Biholde ye the foulis of the eir, for thei sowen not, nether repen, nether gaderen [gather] in to bernes.— Wiclif (1380).
"Beholde the foules of the ayer, for they, sowe not, nether reepe, nor yet cary in to the barnes.—Tyndale (1534).
2.
A corrupted form of Berners.
(The Berners family owned land in Islington, London after the Norman Conquest)

Barn / Barne

Surnames of the United Kingdom by Henry Harrison 1912::

1. English: Dweller at the barn (Middle English berne, Old English bern) as in William de la Berne.
2. Bairn, child (Middle English barn(e) Old English b(e)arn = Scand. barn) Walter le Barne.
3. Old English: person name Beorn =WARRIOR, NOBLEMAN. (Scand.) the Old Norse person name Björn =BEAR.

Barnes

Who Do You Think You Are?  Trace Your Family History Back to the Tudors::

1. Of the barn (barley house), this British surname is often derived from a significant barn in the local region. 

Barnes

The Penguin Dictionary of Surnames::

1. Local name - a surname recording locality or place name 'barns' (strictly speaking barley houses) Old English, locality or place in Surrey; or 'of (i.e. at)  the barn', genitive rather than plural.
2. A surname based on the first name of an ancestor -  (son) of Barne - Barnes, son of Barne.
3. The family name of the barons Gorell.

Fox

 

Surnames of the United Kingdom by Henry Harrison 1912::

1. A nickname or sign-name from the animal (Old English) fox
2. occ. Fowkes or Fawkes = Foulkes.

Gosling

Surnames of the United Kingdom by Henry Harrison 1912::

1. The GOSLING (a nickname) Old English gós, goose + the double dim. suffix -l-ing] 2 for Goslin.

Holloway

Surnames of the United Kingdom by Henry Harrison 1912::

1. Dweller at the HOLLOW WAY. Old English  hol(h, hollow + weg, path, way.
Holloway, London, 'includes the whole district lying in the hollow beyond Islington towards Highgate Hill.'

Parsons

1. the Parson's (son).

Salthouse

Surnames of the United Kingdom by Henry Harrison 1912::

 1. (Eng.) Dweller at a SALTHOUSE (place where salt was made) [Middle.English salthus, Old English. s(e}alt-Ms}

Wooldridge

Surnames of the United Kingdom by Henry Harrison 1912::

1. (with intrus. -d-) for Woolrich. WOOLRICH. 1. (Eng.) for the common Anglo-Saxon. WOOLRIDGE persons name Wulfric = WOLF-POWERFUL [Old English] wulf+ric(e] The 13th-cent. forms of this name were: Wlfric, Wlfrich, Wolvrich, Wulvrich,  
   
  Old English (also called Anglo-Saxon) is an early form of the English language that was spoken in parts of what is now England and southern Scotland between the mid-fifth century and the mid-twelfth century. It is a West Germanic language and therefore is closely related to Old Frisian and Old Saxon. It also experienced heavy influence from Old Norse, a member of the related North Germanic group of languages. It is also closely related to the German and Dutch languages.
Middle English is the name given by historical linguistics to the diverse forms of the English language spoken between the Norman invasion of 1066 and the mid-to-late 15th century.
Source: Wikipedia.