In 1851, we see Francis Knibbs, aged 12, living at Shepton Mallet, Gloucestershire, England with his aunt and uncle George and Selina Witcombe (nee Best) and their son Jonah aged 17. George was a Cabinet Maker.

We assume that these are relatives on his mother Ann's side of the family.
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Francis was quite possibly living in the Kings Arms in West Street, Buckingham in 1864.
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Francis appears in the 1881 census living at 146 Armagh Road, London, England:
Francis E. KNIBBS Head M Male 42 Shadwell, Middlesex, England Publican
Amelia KNIBBS Wife M Female 39 Holborn, Middlesex, England
Francis KNIBBS Son Male 6 Southwark, Middlesex, England Scholar
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Francis can be seen in the 1891 census living at 103 Tredegar Road, Stratford le Bow, London, England:
Francis Knibbs Head 52 Living on own means London St Georges East
Amelia Knibbs Wife 49 London Holborn
Francis Knibbs Son 16 Stationers Assistant London Southwark

also,

Name Relationship Age Gender Birthplace
Francis E Knibbs Head 52 Male St George In The East, London
Amelia Knibbs Wife 49 Female Holborn, London
Francis Knibbs Son 16 Male Southwark, London
Mary Lorkin Lodger 35 Female St Luke, London
Emma Chatterton Boarder 25 Female Birmingham, Warwickshire
Ellen Cooker Visitor 30 Female Hatfield Broad Oak, Essex
Town: Bow and Bromley of the Tower Hamlets, Ecc. Parish: St Stephan, Civil Parish: Stratford Le Bow St Mary, County: London
Registration: Poplar, Bow, 6
Source: PRO/National Archives Reference # RG12/314 Folio 129 Page 10
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Francis died aged 61 years

The 1901 census shows Amelia living in the parish of Stratford Bow, London, England at 103 Tredegar Road, aged 59. Her occupation is given as "Living on Own Means". Living with her is her son Francis, then aged 26.

Amelia is given as her son Francis' next of kin in 1912, during a visit he made to the USA.
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We see Amelia in 1911, living at 103 Tredegar Road, North Bow, Poplar, London, Middlesex, with her son Francis:
Amelia Knibbs Head Widow F 69 Private means Holborn London
Francis Knibbs Son Single M 36 Accountant Beremondsey London
Ann Maria Clarkes Servant Widow F 57 General Domestic Servant Ollbury N Birmingham

This Francis Knibbs travelled to America in 1912. The Ellis Island records show that Francis KNIBBS, aged 37 years and 5 months arrived at Ellis Island, New York on 15 August 1912. He sailed on a ship named Olympic from Southampton. The Ship's Manifest identifies that he was a "Non Immigrant Alien" there for the purpose of "Touring and Looking". He was 5'9" tall, 37 years 5 months old, unmarried, with very fair complexion, fair hair and grey eyes. It says that he was born in London, with the name and address of his nearest relative given as Mrs Knibbs of 103 Tredegar Rd, Bow, London (his mother Amelia).

We know from the 1881 census that this Francis was born in 1875 so the dates would appear to match.

The 1901 census for England and Wales shows no Knibbs other than Francis living with his mother Amelia in the parish of Stratford Bow, London, England.
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In 1911, he was still unmarried and living with his mother at 103 Tredegar Road, North Bow, Poplar, London, Middlesex:
Amelia Knibbs Head Widow F 69 Private means Holborn London
Francis Knibbs Son Single M 36 Accountant Beremondsey London
Ann Maria Clarkes Servant Widow F 57 General Domestic Servant Ollbury N Birmingham
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It's a conjectuire that Francis married Maud A Mead during q3/1919 at Romford District, Essex.