The question being asked can't be scientifically researched until it is pinned down – what is supposed "Euro-English"? I think England is in Europe (still), so the myriad varieties of English of England might seem to be "Euro-English", and likewise Irish, Welsh and Scottish varieties. To rule out that obvious class of dialects, I assume you mean "varieties without native speakers" – stepping out of Europe for a moment, East African and Indian English would thus be outside of the scope of the question.
We can also ask if "UK English" exists (or if "English English" exists); that presumably would mean "Is there a set of features that identify what is common to all speakers in England, or in the UK". The set of features is somewhat small; but to quality as UK English, it ought to exclude features found in other regional Englishes, such as "American" English, Canadian English, Australian English and so on. That is, we need something that makes the language specifically "European", meaning that you are only looking for features of the European dialect – a common set of features shared by non-native speakers of Europe, but not more general (e.g. clausal negation is done with the word "not", the integer that precedes "two" is "one").
This brings us to a possible scientific question: are there any features that exist in the non-native varieties of Europe and are exclusive to that variety? I expect that this question is answered in the negative. First, the dialectal unity of European English is questionable, as is the unity of UK English. Second, the geographical exclusivity of those features compared to other planetary zones is highly unlikely. It is most likely that any entity "Euro-English" would have to be defined with some form of UK English as the standard. And thus the question devolves to the squabble between Mollin and Modiano – there is no testable (refutable) scientific hypothesis on offer.
Rather than asking whether Euro-English exists, you can simply assume that it exists and then ask what properties it has. Those properties may be shared with other dialects of English.