I wasn't aware that Virgin insisted on a UK-issued ATPL. I will try and find out if that is actually the case and, if so, why. I don't guarantee getting an answer - or, at least, one that will help very much. I assume such a restriction, if it exists, is legal; Virgin is not in the habit of using or perpetuating illegal employment practises.
However, it seems to me that the process of converting your licence is straightforward enough, and would be unlikely in itself to prevent employment. If the company liked you enough, it could agree to employ you subject to getting the licence conversion done before you began flying, so I doubt that this is a stopper.
Far more likely, in my opinion (and it is just my opinion!), is that there are sufficient applicants locally (ie within Europe) to not need to look further afield. I can't see any company making things more difficult or expensive for itself than it needs to, and Virgin is way, way oversubscribed for pilot positions. It can take whoever it wants - and that means (among other things) whoever is easiest and cheapest to employ. Sorry if that's not what you want to hear - and please understand that this is purely my speculation, and not some kind of demi-official company statement!
Scroggs