The BBC article seems to be actually reporting on this Ofcom "Draft Initial Obligation Code"
The document says "We welcome responses to this consultation by 30th July 2010."
Also, the OP says "Music and film companies will then be allowed access to the list, and be able to decide whether or not to take legal action."
The full consultation document clarifies this somewhat saying:
ISPs will have to keep a record of the CIRs [Copyright infringment reports] linked to each subscriber along with a record of which Copyright Owner sent the report. A Copyright Owner can request an ISP to provide them with relevant parts of those records on request, but in an anonymised form to comply with data protection legislation. This is called a Copyright Infringement List.