*THIS IS PRE-BREXIT INFORMATION*
(no one knows what will happen after)
As a doctor you are entitled to full registration in any EEA country, provided you are a citizen yourself of an EEA country and you completed your primary training in an EEA country.
The EEA includes: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland (EFTA), Ireland, Italy, Latvia, Liechtenstein (EFTA), Lithuania, Luxembourg, Malta, The Netherlands, Norway (EFTA), Poland, Portugal, Romania, Slovakia, Slovenia Spain, Sweden, and the United Kingdom.
Switzerland also entered the same agreement for full registration in 2002
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Information from the BMA:
https://www.bma.org.uk/advice/career/going-abroad/working-abroad/european-economic-area