Found in the 1881 census!  Living at the Glebe House, Bambrugh, Northumberland with his 30-year-old unmarried daughter Lucy and 5 house servants.  He stated he was married but his wife was not there; the presence of a housekeeper and a cook in the house indicate to me that in fact his wife was not there and that he might just have been a widow.

I wonder if this is his death:

Surname   First name(s)   Age   District   Vol   Page
Deaths Mar 1885   (>99%)
DARNELL William 68 Hastings 2b 32

Yes: see below.
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In 1851 he had the same first five children as in 1861 and additionally he described himself as “MA, JP”.  They were living at Vicarage House, Bambrugh and had a staff of 5.
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In the 1861 census he had his wife and large family with him:

Surname  Forename  Age  Relation  Occupation  Birth Place
Darnell William 44 Head Vicar Of Bamburgh  Stocken On Leeds, Durham    
Darnell Frances 41 Wife Ryton, North Durham
Darnell William 16 Son Scholar   Durham City
Darnell Frances 14 Daur Scholar  Bamburgh, Northumberland
Darnell Mary 13 Daur Scholar -, Durham
Darnell Charles Sharp 11 Son Scholar  -, Durham
Darnell Lucy Elizabeth 10 Daur Scholar -, Durham
Darnell Philip 8 Son Scholar -, Durham    
Darnell Cecil Margaret 2 Daur Bamburgh, Northumberland
Darnell Agnes 2M Daur   Bamburgh, Northumberland

Address: Glebe House
Registration District: Bamburgh, Northumberland
Parish: Bamburgh, Northumberland
Ref:   RG9/3883/~F73

Additionally there were six live-in staff.
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In 1871 he only had his son Charles there plus three staff, no wife and none of the other children.
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In the Durham Baptism register, <http://www.ebooksread.com/authors-eng/durham-cathe...of-christ--hru.shtml> there is this entry:

1850 Sep. 10 Lucy Elizabeth,'^ dau. of William and Frances Darnell ; College,
Durham ; Minister of Bamburgh ; by H. Exeter.

and this note at the foot:

The father was the Rev. William Darnell, born 19 Nov. 1816 at Stockton Vicarage ; of Christ Church, Oxford (B.A. 1838, M.A. 1843); Vicar of Bamburgh, Northumberland; J.P. The mother was the eldest dau. of the Ven. Charles Thorp, D.D., Archdeacon and Prebendary of Durham, and Rector of Ryton ; married at Ryton 2 Jan. 1844. [MS. Ped. by E. A. W.]

There is also a note in the register on William’s father:

The father was the Rev. William Nicholas Darnell, B.D. ; he was baptized 16 April 1776, at All Saints, Newcastle ; of Christ Church College, Oxford (B.A. 1796, M.A. 1800) ; Rector of St. Mary-le-Bow, Durham (June 1809) ; Vicar of Stockton-on-Tees ; Prebendary of Durham (Jan. 1816) ; Rector of Stanhope, succeeding Bishop Phillpotts ; died there and was buried at Durham Cathedral 24 June 1865, set. 89. The mother [Elizabeth] was the eldest dau. of the Rev. William Bowe, M.A., of Scorton, co. York ; married 15 June 1815 ; buried at the Cathedral 7 April 1864, set. 76. [MS. Fed. by E. A. W.]
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From Durham Record Office <http://nd.durham.gov.uk/recordoffice/register.nsf/...;Highlight=0,burrell>, there are these entries in the Durham Directory

DARNELL, Rev. William, forty-one years vicar of Bamburgh
died 9 March 1885 (Durham Directory, 1886)

DARNELL, Mrs. (widow of Rev. William Darnell [q.v.])
died 8 August 1912 (Durham Directory, 1913) see M29/1

DARNELL, Rev. W.N., rector of Stanhope
died 19 June 1865 (Durham Directory, 1866)

They confirm the data I found on FreeBMD. and the last entry is that for William’s father ‘William Nicholas Darnell’.
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Foster’s Alumni Oxoniensis reports:

Darnell, William 1s. William Nicholas of Stockton, co Durham, cler.  COPPUS CHRISTI COLL., matric 7 April 1835, aged 18; B.A. 1858, M.A. 1843, chaplain to the Duke of Buccleugh 1839, [TFPL: whose mother-in-law was Elizabeth Powys], vicar of Bambrugh, Northumberland, 1841-82, died 9 March 1885.
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Their marriage, noting that Ryton is an area of Gateshead district and that in the censuses her first name is always Frances.

Surname   First name(s)   District   Vol  Page
Marriages Mar 1844   (>99%)
ANDERSON Isabella Gateshead 24 111
Callender Edward Emerson Gateshead 24 111
COMB Janet    Gateshead 24 111
DARNELL William    Gateshead 24 111
GLASPER Barbara    Gateshead 24 111
MARCH John    Gateshead 24 111
NATERS George    Gateshead 24 111
THORP Frances    Gateshead 24 111
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