I think that lawyers could possibly occupy an entire conference with discussing the issues here.
Your 'criminal record' (i.e. the data held by the Criminal Records Bureau and on the Police National Computer) is, indeed, 'private' information and subject to the controls of the Data Protection Act.
However, court records are public documents. Anyone can normally sit in a court and take notes about convictions and sentences. Further, anyone can visit a court and consult the court register, which lists all convictions and sentences relating to cases heard before that court. Similarly, the press (with very few exceptions) are free to publish that information.
I suspect that the court official has not contravened the Data Protection Act, simply because he has only conveyed 'public' information to your partner. However he may have breached rules laid down by his employer.
Chris