I haven’t read through all the posts here, but my suggestion would be contact YOUR bank and have your bank contact them. If anyone can be pissy and demanding, banks can. Let them get to the bottom of this situation.
Sorry TaxGuy, but are you informed about EU law at all? If not, I respectfully ask you to take your own advice if you want to discuss the legal question whether such a rule exists. As Random made clear, even your ‘advice’ on the possibility of being ‘scammed’ was also incomplete, to put it mildly. 
Since no-one provided more than an estimate, it is entirely proper to provide information to help the OP to asnwer the question. I added an educated guess (and said that I didn’t know for sure). I’m a practicising lawyer, do have knowledge of EU law, have worked with a bank in the past with international funds transfers, and have my experience as a private person. I’ve never seen evidence of such a rule and have never had to provide or ask for such information. Doesn’t mean that it or something like that doesn’t exist, but makes it unlikely. A search in EU rules is really difficult if you don’t know exactly what to look for. It could be there is some recent new rule related to anti-terrorism, but it seems unlikely that this would necessitate you to provide your own phone number if the other party wants to send you money.
If the bank wants that information for other reasons, they can try to ask for it, but that doesn’t mean that they are obliged to ask for it because of an EU regulation.
Cuckoorex, you do what you want, but I still feel I should repeat my warning for caution. I don’t see why you would have to give more than your account number, home address and bank details. Why do they need your phone number?
I should add that if TaxGuy only took offense to my use of the word ‘bullshit’, I do apologize. That word may well be too strong, especially for GQ. I plead ignorance (English is not my first language, so the word may be stronger than I realized), and I thought I’d follow a previous poster.
I only wanted to say that I did seriously and with some reason doubt whether a regulation asking you for information including your phone number exists. Should have chosen my words more carefully. Sorry.
Tusculan I’m kinda trying to read minds here, but it looked to me like Taxguy was referring to JerzyBulowski’s comment. The one which added nothing to the discussion.
I could be wrong though…
Thanks for the kind words, whatami. However, Taxguy specifically used the plural.
I’m still a bit miffed about the utter gall with which he dared in one and the same post acknowledge his own misinformation and accuse others of the selfsame ignorance. Well, as they say, you shouldn’t let strangers at message boards get under your skin. 
By the way, when I asked my bank’s employee about the process, they provided me with the bank’s “Swiftcode” which apparently is used in place of the bank’s routing number sometimes with international money transfers…like I said, the bank employee seemed completely unfazed by the situation and didn’t seem to think that there was really any cause for concern.
The SWIFT code is a code assigned by the SWIFT organisation to banks. SWIFT manages the electronic network used by banks (and some multinationals) to transfer funds. The code is necessary to transfer funds between one bank to the other: it identifies the receiving bank (there is a ‘phone book’ for the codes of all member organisations of SWIFT, so this is kinda public information). The receiving bank still needs additional information to be able to determine the account to which they have to credit the incoming transfer. The SWIFT message that is sent has an additional information field for exactly this kind of information. Providing this basic information is indeed normal.
As I tried to say, providing you bank’s details is no problem, providing your account number and name should not be a problem. However, providing your telephone number is AFAIK unnecessary, both for practical purposes and for legal reasons. The receiving bank can verify whether the account number is correct by checking the recipient’s name. No need for phone number, or even address. That is what triggered my suspicions.
I recently did order an international transfer (admittedly within Europe) and there was no need to provide the other party’s telephone number. The transfer did arrive correctly.
Well, after all is said and done, I wouldn’t touch that with a ten foot pole.
In any case, the client already had my phone number, address, and email address; that information is routinely exchanged between me and my freelance clients anyway.