Virgin Media claims that the campaign is "educational" in nature, despite threatening users with disconnection in a warning on the envelope.
However, the ISP conceded that the warning on the envelope was a "mistake" and pledged to review its campaign next month.
"This is about education. We make no assumptions about who is at fault. It may be someone in the family or someone illegally using their Wi-Fi connection, " said a Virgin Media spokesman.
The BPI explained that "thousands more" letters will be sent as part of the organisation's wider plans to introduce a 'three-strikes' policy which could ultimately result in repeat offenders being disconnected.
Virgin Media is the only ISP to back the BPI's campaign thus far. Some service providers, such as Carphone Warehouse, have refused to participate.
ISPs have until next spring to confront illegal file-sharing over their networks or face government intervention to force them to take action against repeat offenders.