Illegitimate son of Caroline Knibbs, single woman, and we think, a man named Frank French.
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The 1871 census for Oxfordshire and North Berkshire shows Frank as living at Swerford.
Frank F KNIBBS 2

This is taken from a KNIBBS extract of the census. Clearly, at the age of 2 years he couldn't have been living alone. His mother Caroline was living at Chapel Brampton, Northamptonshire, and working as a live-in housemaid, so I am not sure who was looking after Frank but it would seem that it was someone other than a Knibbs.
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Frank appears age 11 in the 1881 census living with his grandparents William and Emily at Village Blue Row, Swerford, Oxfordshire. By this time, his mother Caroline had married George Hilton, had two more children, and was living in Lewisham, Kent.
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Frank appears in the 1901 census aged 32 years, living at Lewisham, London, England.
Frank Knibbs 32 Oxon Siverford London General Labourer
Mary Knibbs 34 Wilts Chippenham  
Elsie Knibbs 4 Kent Sydenham London  
Frances Knibbs 2 Kent Sydenham London
Bessie Knibbs 9M Kent Sydenham London
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We can see Frank and his family in 1911 living at 4 Rowland Grove, Wells Road, Sydenham in the Lewisham District of London:
Frank French Knibbs Head Married 42 General Labourer Swerford Oxon
Mary Knibbs Wife Married (15 years) 44 Wiltshire Langley
Frank Bertram Knibbs Son 7 Sydenham Kent Buval
Frances Mary Knibbs Daughter 12 Sydenham Kent Buval
Bessie Kathleen Knibbs Daughter 10 Sydenham Kent Buval

Sadly, not much is known about the background of Mary. If indeed the 1901 census is correct, and she is from Chippenham, Wiltshire, then the 1881 census indicates that she was from a pretty wealthy background. Her father Thomas Ferris farmed Corton Farm, Calne in Wiltshire which had some 600 acres, employing 12 men and 4 boys.

Thomas M. FERRIS M Male 46 Chippenham, Wiltshire, England Farmer 600 Acres 12 Men & 4 Boys
Harriett FERRIS M Female 50 Chippenham, Wiltshire, England
Emma FERRIS U Female 22 Chippenham, Wiltshire, England
Mary FERRIS U Female 17 Chippenham, Wiltshire, England
Thomas W. FERRIS U Male 15 Chippenham, Wiltshire, England Farmers Son
Charley H. FERRIS Male 13 Chippenham, Wiltshire, England
Martha F. FERRIS Female 12 Chippenham, Wiltshire, England
Francis E. FERRIS Male 10 Chippenham, Wiltshire, England
Walter J. FERRIS Male 8 Chippenham, Wiltshire, England
Kate STRANGE U Female 22 Chippenham, Wiltshire, England (Dom)
Mary A. TAYLOR U Female 19 Chippenham, Wiltshire, England (Dom)
William WHEELER U Male 17 Chippenham, Wiltshire, England Farm Servant (Indoor)