The British Newspaper Archive is searchable online and has yielded a number of references to Brinston both as a surname and a place name.
Police Sergeant Brinston is mentioned in a number of stories from Hampshire in the south of England, the first in June 1860 when he is described as locating the nephew of a woman who died suddenly while passing through the town of Odiham. Two years later he and three constables attempted to save assets from a farm fire at Crundall. In December 1865 Sergeant Brinston was mentioned in a court case involving the concealing and destruction of a will. In July 1867 he was cited regarding boot tracks at the scene of a robbery. In November of that year Police-Sergt. Brinstone (sic) testified in a case in which a man was convicted of stealing a bushel of wheat and sentenced to six weeks' hard labour. In an 1862 case involving theft from the premises of a watchmaker there was reference to Police-constable Brinston. This could be someone else but more likely an error was made in recording the officer’s rank.
In August 1891 a case was reported in which it was stated: “Superintendent Brinston, stationed at Aldershot for the past six years, said he heard screams in the police passage on tbe night of June 15.” It seemed the sergeant had been promoted but what evidence exists to help decide if both were the same man? 
The 1871 census for Lymington, Hampshire includes the household of Robert Augustus BRINSTON, aged 37, a police sergeant who was born in Christchurch, Hampshire. In the household at Gosport Street Police Station are Robert’s wife and 4 children plus two single police constables. I could not find Robert Brinston in later census records. However, in the 1891 census, I found Robert A. BRINSON, Superintendent of Police, resident at the Police Station in Aldershot in the County of Surrey. He was 57 and his birthplace was Christchurch, Hampshire. In the household were Robert’s wife, 3 children, 8 constables and one prisoner. 
In the 1911 census Robert Augustus BRINSON, 77, police pensioner, shows up in Melcombe Regis, Weymouth, Dorset with his wife of 53 years and two of their unmarried adult children. For this enumeration we can see the actual census schedule that someone in the family completed and the name is clearly BRINSON. I wondered about other records and found some. Robert Augustus BRINSON was baptized on 12 April 1835 in Christchurch, Hampshire and his birthdate given as 6 Aug 1833.
Indicative of how confusing names and handwriting can be, Robert’s marriage is indexed both as Robert Augustus BRINSON and Robert Augustus BRIMSON – apparently the transcriber could not decide between those possibilities. Robert married Mary FELTHAM in the quarter ending Dec 1857. Their son Robert Augustus BRINSON was born on the Isle of Wight and his birth registered in the quarter ending June 1858, all consistent with census data. 
Yes, the sargeant got a promotion but the newspapers had been spelling his name wrong during all those years. He was always a BRINSON not a BRINSTON.
 The British Newspaper Archive (http://www.britishnewspaperarchive.co.uk/ : accessed 03 Aug 2014), as follows. Odiham: Fatal Accident. Reading Mercury, Berkshire, England, Saturday 09 June 1860, page 4. Fire at Crundall. Aldershot Military Gazette, Hampshire, England, Saturday 14 June 1862, page 3. Hampshire Winter Assizes: Crown Court Saturday, Concealing a Will. Alnwick Mercury, Northumberland, England, Saturday 16 December 1865, page 3. Hants Summer Assizes: New Forest Burglaries. Hampshire Advertiser, Hampshire, England, Saturday 20 July 1867, page 11. Stealing Wheat at Eversley. Aldershot Military Gazette, Hampshire, England, Saturday 30 November 1867, page 3. Hants Winter Assize: Larceny. Hampshire Advertiser, Hampshire, England, Saturday 13 December 1862, page 3. Hampshire Summer Assizes: Crown Court—Tuesday. The Aldershot Perjury Case. Hampshire Advertiser, Hampshire, England, Wednesday 05 August 1891, pages 2, 3 & 4.
 1871 England, Wales & Scotland Census, Hampshire, Town of Lymington, Parish of Lymington, Enumeration district 3d, Piece 1173, Folio 43, page 15, lines 11-18 , Gosport Street Police Station, Robert Augustus Brinston household; digital image, Find My Past, (http://www.findmypast.co.uk/ : accessed August 4, 2014); citing RG10, Piece 1173, Folio 43, page 15.
1891 England, Wales & Scotland Census, Surrey, Town of Aldershot, Parish of Aldershot, Enumeration district 5, Piece 564, Folio 18, Page 30, lines 17-30, The Police Station, High Street, Robert A. Brinson; digital image, Find My Past, (http://www.findmypast.co.uk/ : accessed August 4, 2014); citing RG12, Piece 564, Folio 18, Page 30.
 1911 Census for England & Wales, Dorset, Melcombe Regis, 19 Avenue Road Weymouth, Robert Augustus Brinson household, Findmypast.co.uk, (http://www.findmypast.co.uk/ : accessed August 5, 2014), RG14PN12341 RG78PN702 RD263 SD2 ED2 SN233.
Hampshire baptism transcriptions, Find My Past, (http://www.findmypast.co.uk/ : accessed August 5, 2014), Robert Augustus Brinson, 12 April 1835; citing Christchurch, Hampshire, England.
 Free BMD. (http://www.freebmd.org.uk/ : accessed 05 Aug 2014).