Is it possible for a German physician qualified to the level of
"Facharzt für Allgemeinmedizin" to gain recognition as a "General
Practioner of Medicine" in accordance with European Law but without
having to practice in the UK?

Tina,
From the way you state your question, I assume that you know that it
is possible for German MDs to work in the UK, but after gaining some
recognition of their qualifications, so I expect that you are asking
if a Facharzt (specialist) can be immediately employed or set up a
practice if he or she "down-grades" to GP.

Perhaps these sites can help you:
http://www.germanmedicine.net/en/index.html
http://www.med-jobs.de/german/seite_3_aerzte.htm
http://www.kwp-consult.de/jobs-fuer-aerzte/0/?suchbegriff=auslandsjob

Maybe a Researcher can give you more specific information.
Regards, Myoarin