Data Protection Act 1998 s.1 is entitled "Basic interpretative provisions"
Data Protection Act 1998 s.1(1) provides that:
"'data processor', in relation to personal data, means any person (other than an employee of the data controller) who processes the data on behalf of the data controller"
There is more detail in the useful publication, "Data Protection Act 1998 - Legal Guidance" issued by the Information Commissioner.
The Information Commissioner's Office Technical Guidance Notes webpages are an essential source of practical information on all aspects of data protection.
See notes generally at Data protection .