Are companies in the United Kingdom entitled to make data subject access requests, or is this right limited to non-companies such as individuals?
Which statute permits or prevents them from doing so?
No. The Data Protection Act 1998 provides a 'Right of access to personal data' to "an individual". See Section 7, subsection 1.
Although the word 'person' can mean a company in a legal context, the word 'individual' does not.