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I now find that the Ordnance Survey say it has "Place type: Valley" [1].
I cannot find any evidence that people there use the name Ballingdon Bottom. There is evidence for the area being considered part of Gaddesden Row or of Jockey End, but there is no agreement about which areas are hamlets. The Royal Mail postcode finder [2] gives all the addresses as "Clements End Road, Gaddesden Row, HEMEL HEMPSTEAD, HP2 6HX". Google defines Jockey End to include the area [3]. Great Gaddesden parish council [4] just says there "are the villages of Great Gaddesden and Gaddesden Row and the hamlets of Bridens Camp, Water End, Noake Mill and St Margarets".
I now agree it is notable because of the administrative history added by User:Stortford.
I have changed the article to say valley instead of hamlet.