You can get short term permissions to operate an American experimental category aeroplane in the UK or most other European countries. The UK will normally give you 28 days in a given year, and it can potentially be extended to 90. However, it's not a long term solution, and not a European solution - such aeroplanes are sub-ICAO, and so each country will have to give individual permissions.
I would advise against it as a solution of your normal flying. If you want a Kitfox, or anything else that's sub-ICAO, buy something with your local national registration and approval already.
G