The name Redknapp, (also spelled Redknap, Rednap and Rednup) is derived from the colour Red and the old English “cnaep” or “knap” meaning a hillock or brow of a hill, but also a 15th century slang word for “head” as in “the knap of the case” for the head of the house. So “Red Knap” could either mean someone who lived on the “red hill” or much more likely, the person with the “red head”, and given the colouring of a number of bearers of this name the likely derivation is fairly obvious.
Although there had been one instance of the name being spelled with two “p”s in the late 1700s, and various spellings with one and two “p”s and an “e” on the end in mediaeval times, this Redknapp family’s original name was spelled Redknap with one “p” for the whole of the 19th century, and only acquired the extra “p” as a standard spelling at the beginning of the 20th century when many names in working class families became fixed in their spellings. This was because from 1870 an act of parliament brought in compulsory schooling for children, and so all children (who actually went to school) were taught to read and write in Great Britain from that point on, and so would spell their name the way they first saw it written by an adult, their school teacher, that school teacher would spell the name however they felt like spelling it unless they were aware of how the local vicar would spell it in the Parish Registers, and that particular way of spelling the name would stick going forward, more of less unchanged to the present day.
Harry Redknapp’s branch of the family are most likely descended from Redknaps who were Mercers in late Mediaeval London. Mercers were high status traders, the word being derived in English from the Old French Mercier (ultimately derived from the Latin Merx – trade goods, the same root as Merchandise). There were a number law disputes naming London Redknaps in various court cases over trading and trade goods, a long tradition that would carry on down through the generations, this and indeed the origins of the nickname Red-Head (Red-Cnaep) was undoubtedly a notable identifier of the Red Headed English RedKnaps amongst the dark headed French Mercers they competed with.
It’s not hard to see where a link with trade in London turned into a link with the transportation of trade along London’s River, and Harry’s branch of the family were part of an extended family of Thames Watermen and Lightermen (Watermen rowed boats to carry people on the Thames, and Lightermen specifically rowed “Lighters” which were large flat bottomed barges) living on both banks of the Thames both on its western reaches of the “Surrey Side” and London, and on the central and Eastern regions of the “Middlesex Side” depending on the availability of work. their work was essential to the maintenance of the passage of goods and people through London before bridges and roads of the Victorian era started to devalue them.