I would suggest that you discuss this with the Information Commisisoners on 01625-545700.(posted 8067 days ago)They will advise you if this is right. I suspect that they will ask you to issue a SARN against the other company, but they might also ask you to send in an assessment request.
This is free, the IC are helpful, the IC are the Sun-Source of information about the Data Protection Act. Do it.
Good Luck.