Salwey was the son of Humphrey Salwey of Stanford Court, Stanford-on-Teme and his wife Anne Littleton, daughter of Sir Edward Littleton.
Sir Francis Winnington (1634–1700) Solicitor-General to King Charles II, acquired the family seat of Stanford Court, Stanford on Teme, Worcestershire through his marriage to Elizabeth, third and youngest sister and coheir of Edward Salwey.
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