Although eSnips removed the material, the site was unwilling to provide its members' contact details without a court order.
Steven Maier, of Manches LLP, the estate's UK solicitor, said: "The Tolkien estate has a duty to protect the copyright in Tolkien's much-loved works and cannot allow the posting of illegal downloads on file-sharing sites."
Maier added that further legal action against individuals was unlikely, except in the case of persistent offenders.
"We are sensitive to the fact that many of the eSnips members are Tolkien fans who were not seeking any commercial gain," he said.
"However, we need to make it clear to these individuals that the estate will not tolerate the posting of illegal copies of Tolkien's works by anyone."
This type of action is nothing new to the Tolkien estate. Last month it obtained agreed damages of $4,000 from an IT professional in Milwaukee who repeatedly offered Tolkien's works for download.
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