There does not seem to be a birth/baptismal record for William Parham in Wiltshire. Possibly the same as William, born 29 May 1753 in Mark Somerset, son of William Parham and Ann.
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In 1812 William Parham was named in the Will of his father-in-law Bartholomew Horsell Senior of Nore Marsh in the Parish of Wootton Bassett, yeoman, as husband of Bartholomew's daughter Mary.
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William Parham of Purton, husband of Mary, died aged 83 years (MI, burial record).
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Abstract of the Will of William Parham of Purton in the County of Wilts, Yeoman, written 26 May 1830, proved 29 Jun 1836. 4
Acknowledges that he owes £300 to his brother-in-law Bartholomew Horsell.
Gives, devises & bequeaths to his daughter Elizabeth Warman and his son-in-law Jasper Warman all his freehold messuages, lands, tenements and hereditaments in the parish of Wootton Bassett in Trust, and all his personal estate whatsoever.
Gives to his daughter Eugenia Rolfe the wife of William Rolfe a legacy of £300, for her own sole and separate use.
Gives to his friends Richard Whatley of Cheltenham in co. Gloucester, Gentleman, William Yorke of Cirencester in co. Gloucester, ironmonger, and William Warman the Younger of Wootton Bassett, grocer, a legacy of £500, in Trust for the benefit of his children and their heirs.
Gives and devises to his sister Mary Harrison an annuity of £20, in lieu of a debt of £200 he owes her. If she refuses this arrangement then he wills that she will not be entitled to the annuity and will be paid the £200 he owes her.
Nominates and appoints his said daughter, Elizabeth Warman, and his son-in-law, Jasper Warman, co-executors of his last will and testament.
Signed
James Bradford, A. P. Burt, Thos. Jefferies