A Vision of Britain through Time provides the following description of Barford from John Marius Wilson's Imperial Gazetteer of England and Wales of 1870-72:
Until the Dissolution of the Monasteries (circa 1535-1541) Barford was considered to be a chapelry. It was made an ancient parish at the Dissolution and this status continued until 1625 when it was made an extraparochial area until 1858. From 1858 until 1935 it was a separate civil parish in Kettering Rural District. In 1935 it was absorbed into the nearby parish of Rushton. Since 1974 it has been part of the Kettering District of Northamptonshire.
There is no article in Wikipedia. In the article on Rushton, however, it refers to An Inventory of the Historical Monuments in the County of Northamptonshire, Volume 2, Archaeological Sites in Central Northamptonshire provided by British History Online. The consensus appears to be that Barford was a deserted village. There is no information in A Vision of Britain through Time to state what other parishes, besides Rushton, Barford might have had links with.