If you employ a freelancer on a regular basis (every week), do they automatically become an employee??

Or can they still work as a registered self employed person?

You will find that there is no easy answer to this.

The documents that you need to read (and get confused by) are on the Inland Revenue website and are
IR56 - Employed or self-employed? (http://www.inlandrevenue.gov.uk/pdfs/ir56.htm)
and
IR148 - Are your workers employed or self-employed? (http://www.inlandrevenue.gov.uk/pdfs/ir148.htm)