Official EASA worded rule is operator based or residing in the EU
UK CAA rule is wrongly interpreted to include third country operators with aircraft based in the UK (even temporarily) however they haven't corrected this yet.
Other EU countries also interpret it wrongly to include pilots based / living in their EU country.
Finally, if you fly N reg in the EU you are in a legal mess. The new regs would essentially leave you without a valid licence, FAA or EASA.
The EASA licence is only valid to fly N reg in the EU country that it is issued, so you would need a separate EASA licence from every other EU country you fly into. (See FAA legal decision below)
http://www.faa.gov/about/office_org/...rpretation.pdf
And of course EASA / individual CAA's are trying to restrict FAA licence holders in the same way, even though their licence is from the legal state of registry