In reply to MONONOKE: There are two aspects to your question.
1. Is the qualification a European qualification or a UK qualification? (From The CWA course details, 'Remit':- 'It is valid throughout the UK.')
2. Is it possible to use a UK qualification in Europe?
When you describe Europe, I understand that you are talking about the EU countries; I would suggest that you look at the EU laws which harmonise working practices and qualifications within the European Union. My understanding - which may be incorrect - is that individual countries still retain the rights to insist on minimum standards for professions, which is how the French employ the process of 'Equivalence' to ensure that all who seek to work in France are appropriately qualified and experienced.
Perhaps the best UK contact, would be Steve Long (via Siabod Cottage) who is the Chair of the UIAA Training Standards group.
In terms of general comments, which have held true for a number of countries and colleagues who have applied to work in them using their UK qualifications:-
1. Does your intended country operate a similar qualification?
2. Is the profession of instructor regulated, and by whom?
3. Is the country a member of the UIAA? (See note about Steve Long, above)
In terms of general principles, at the very least, I would expect them to compare the CWA syllabus (translated at your cost) with their own nearest compatible qualification (which you would reasonably identify for them), and you would probably need to demonstrate other specific competences (language skills, knowledge of particular features of that country's working practices, etc) to satisfy their awarding body.
