Check Six!
Here's a quick and hopefully not too brutal response.
No license, FAA or other, can be directly converted to a JAA license unless the civil aviation authority of the issuing state becomes recognized by the JAA (i.e. Italy is now in the process of becoming a fully recognized JAA state and thereafter all licenses will be automatically converted to JAA after some "in house" JAR training etc).
You would be required to take ALL the exams which can get very costly. Oxford is a good school and you may take some exams via correspondance but not the finals. You would have to attend, I believe, at least a two-week course and final exam phase.
Before you dive into this, however, think twice. To be hired in Europe you need a current FULL European ATPL or a JAA Frozen (writtens completed) ATPL. The practical portion is then done from within the company after hiring and line flying. You also need either a European passport or a working visa (difficult to obtain for us yanks, I have dual citizenship by marriage).
As usual, the European system is complicated and expensive. As dismal as the situation in the States may seem, it's even more difficult to be hired here without the license and type ratings.
Best of luck and feel free to ask any more info as required. Sorry to be the bearer or negativity but better the truth than a possible maybe. I would still contact the Oxford school for more info. They're really nice and helpful folks. Maybe the Brits can get you a working visa but I don't think so. There's a Brit working with me in Italy and he's somewhat distraught that he can't get a visa to work in the States.
Good luck.
Sodapop