The Parish is actually two: Ashfield and Thorpe, each having Church buildings. Ashfield Church and churchyard are in use, but Thorpe Church is long disused.
The picture here is of Ashfield Church, above a drawing by John Western:
The ruins of St Peter's, Thorpe, are by Thorpe Hall, about a mile from the centre of Ashfield. Now all that remains is a round tower some 40 feet high.
The present Ashfield Church of St Mary was build in the middle of the 19th century, on the site of an earlier church that fell into ruins in the first half of the 18th century. In the interim Thorpe Church was used before it, too decayed.
Some years ago, Commander Helps, late of Thorpe Hall (by Thorpe Church), carried out some research on the history of the buildings. The links on the left lead to the information he found about each church.
For further information see also the Ashfield entry in the Simon's Suffolk Churches web site.