In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Bramshaw like this:
BRAMSHAW, a parish in the district of New Forest, and counties of Hants and Wilts; 5 miles SSW of Dunbridge r. station, and 6½ NNW of Lyndhurst. It includes the hamlets of Fritham and Furzley; and has a post office under Lyndhurst. Acres, 3,560. Real property, with West Wellow, £3,194. ...
Pop., 746. Houses, 167. The property is subdivided. Bramshaw House is a chief residence. The Hants portion, amounting to 1,960 acres, is all in the New Forest. The living is a vicarage in the diocese of Salisbury. Value, £161 * Patrons, the Dean and Chapter of Salisbury. The church is a neat, ancient, modernized structure, said to have been built by the Conqueror; and has a square, brick, ivy-clad tower.
GB Historical GIS / University of Portsmouth, History of Bramshaw, in New Forest and Hampshire | Map and description, A Vision of Britain through Time.
Date accessed: 27th April 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Bramshaw ".