Looking at the 1665 Hearth Tax at Penton Mewsey there are the following heads of household:
John Blake is the only Blake family listed at Penton Mewsey in 1665.His descendants baptized there are Joseph (b 1659) and Elizabeth (b 1651). Another John and Em Blake are baptizing children between 1693 and 1706 and these children are: John, Joseph, Sarah, Ann, Thomas and William. Joseph (b 1659) could be the father of John baptizing children later although it is a rather short generation. Once I have extracted all the Blake families from the various registers I might have an answer. But there isn't a Joseph Blake at Andover in this time period baptizing children.
Hence my hypothesis of a couple of days ago is partly flawed. However, the will of John Blake does appear to look at the Robert Blake/Elizabeth Russell family of Andover. I wonder why the name Sacheverell enters the Blake family?