This date is not a match perhaps this baptism is for an older sister who did not survive childhood.
Parish Records, St. Mary Sunbury on Thames, Richmonds upon Thames
Private baptism October 11 1851 Williamina Anderson, parents Eustace and Williamina Anderson of Spelthome Grove, father quality esquire, ceremony performed by H. Vegni

In the 1861 census 2 Strowan? Villas, Morthlake, Surrey
Head Eustace Anderson, age 41, solicitor, born Chelsea, middlesex.
Wife Williamena Anderson, age 37, born Scotland.
Son John E. Anderson, age 17 solicitor’s clerk, born Southampton, Hampshire
Son Eustace Anderson, age 15 solicitor’s clerk, born Charlton, Kent.
Son William E. Anderson, age 13, scholar, born Greenwich, Kent.
Son David Anderson, age 6, scholar, born Mortlake, Surrey.
Daughter Williamina Anderson, age 4, scholar, born Mortlake.
Daughter Elizabeth L. Anderson, age 10 months, born Mortlake.
2 servants.

In the 1871 census No. 10 St. Leonards, Mortlake, Surrey.
Head Eustace Anderson, age 51, solicitor, born Chelsea, Middlesex.
Wife Williamina Anderson, age 47, born Scotland.
Son John E. Anderson, unmarried, age 27, solicitor, born Southampton, Hampshire.
Son Eustace Anderson, unmarried, age 25, solicitor, born Charlton, Kent.
Son William E. Anderson, unmarried, age 23, drawing student, born Mortlake.
Son David Anderson, age 16, Law student, born Mortlake.
Daughter Williamina Anderson, age 11, scholar, born Mortlake.
Daughter Elizabeth L. Anderson, age 10, scholar, born Mortlake.
Daughter Rosa V. J. Anderson, age 6, scholar, born Mortlake.
3 servants.

In the 1881 census St. Leonards, Mortlake, Surrey.
Head Eustace Anderson, age 61, solicitor Major commanding Victoria Rifles Volunteer Corps., born Chelsea, Middlesex.
Wife Williamina Anderson, age 57, born Scotland.
Son John E. Anderson, unmarried, age 37, solicitor and Lieutenant in the Victoria Rifles, born Southampton, Hampshire.
Son Eustace Anderson, age 35, unmarried, solictor and Lieutenant in the Victoria Rifles, born Charlton, Kent.
Son William E. Anderson, unmarried, age 33, [his occupation is crossed out], Greenwich, Kent.
Son David Anderson, unmarried, age 26, [occupation crossed out], born Mortlake.
Daughter Williamina Anderson, age 24, [occupation crossed out], born Mortlake.
Daughter Elizabeth J?, Anderson, unmarried, age 20, [occupation crossed out], born Mortlake.
Daughter Rosa V. J. Anderson, age 16, scholar, born Mortlake.
2 servants.

Parish Records St. Mary, Mortlake, Surrey
Marriage December 31 1885
Frank Robert Cocks, age 29, bachelor, Clerk in Holy Orders, residence Guildford, father Should? Lincoln Cocks, publisher and
Williamina Anderson, age 29, spinster, residence Guildford, Father Eustace Anderson, Major Victoria Rifles
after Banns by Reverend Whittim Sim [Sr?]
In the presence of Eustace Anderson, Rose Victoria Jane Anderson and Charles John Thomson

In the 1891 census The Rectory, Upton, Huntindonshire
Head Frank R. Cocks, age 33, Rector of Upton and Coppingford, born Bayswater, London
Wife Williamina Cocks, age 34, born Mortlake, Surrey
Daughter Ethel L. W. Cocks, age 4, born Stoke, Surrey.
Son Cyril A. Cocks, age 2, born Guildford, Surrey
Son Gilbert A. Cocks, age 1, born Guildford, Surrey
4 servants

Parish Records St. Mary, Horsell, Surrey
Williamina Cocks, residence Upton The Ridgeway, Horsell, buried May 18 1931, ceremony by N. Pares, Vicar

National Probate Calendar
Williamina Cocks of Upton Horsell Ridgway Woking Surrey (wife of the reverend Frank Robert Cocks) died 13 May 1931 Probate London 20 June 1931 to the said reverend Frank Robert Cocks clerk. Effects 8352 pounds.

Vicar of New Buckenham 1896 to 1909.

In the 1901 census
King Street, New Buckenham, Norfolk
Head Frank Cocks, age 43, Clergyman/Church of England, born Bayswater, London
Daughter Margaret Cocks, age 8, born Upton, Huntingdonshire
Son Percy Cocks, age 4, born Upton, Huntingdonshire
Daughter Constance Cocks, age 3, born New Buckenham, Norfolk
Daughter Ella Cocks, age 1, born New Buckenham, Norfolk

UK Incoming Passenger Lists
Embarked Jamaica, departed New York, New York on the Tagus, arrived June 13 1910 Southampton, England, first class
Frank Robert Cocks
Margaret Lincoln Cocks

UK Incoming Passenger Lists
Embarked Kingston, Jamaica on the Samite, arrived Avonmouth, May 14, 1922, 1st class, proposed address Upton Horsell, Woking
Frank Cocks, Priest, age 64
Ella Cocks, age 22, no occupation

UK Incoming Passenger Lists
Departed Kingston, Jamaica on the Jamaica Progress, arrived London, England on September 19, 1933.
Frank Robert Cocks, Upton Horsell, Woking, 1st class, Clerk in Holy Orders, age 76, country of last permanent residence England.
Patricia Anderson Cocks, Winchester House, St. Leonard’s on Sea, school, 12 1/2, country of last permanent residence Jamaica.
Frank Peter S. A. Cocks, Old School House, Holt, Norfolk, school, age 11, country of last permanent residence Jamaica.

In the April to June 1934 marriage index Frank R. Cocks and Grace R. Barton, Surrey, North Easter, Surrey, volume 2a, page 751

1939 England and Wales Register
“Upton” The Ridgway, Woking, Surrey
1. Frank R. Cocks, born July 3 1857, married, clerk in holy orders (retired)
2. Grace R. Cocks, born September 16, 1874, married, unpaid domestic duties
3. Ella A. Cocks, born November 3 1899, single, incapacitated
4. Francis E. Cocks, born June 7 1901, single, unpaid domestic duties
5. Ellen Coman, born July 3 1890. single, cook