I have to help someone set up an online data backup functionality... They only need to backup a few desktops, and the data volume is rather small (a few GB a month at most), but since they are in the financial services business, data security is critical (and for that reason, simple external HD systems will not cut the mustard).

They are obviously not keen to make the acquaintance of the US authorities, so would really like the data to remain in the EU.

Anyone know of a good service? I know about Carbonite and Mozy and Dropbox etc, but they are all US based.

These services are not backup services, they are remote storage.
Backup services will have a universal client that actually backs up data , and stores it in generational format so that file versioning is achieved.

Be clear about your requirements, do you need an off site copy of local storage , or the ability to restore to a point in time, any specific file, or do you need synchronisation of remote storage between clients , or do you need to move off local storage onto cloud storage ? Many options are available.

For Security and Professionalism, I would recommend that you consider a Virtual Private Server, under your full control, preferably with mirrored contingency/backup data centers. This would allow you to use rsynch and rcopy commands to copy local files to your remote server, if you get a VPN sorted, you can have the server present it's remote storage as a local drive on the PC and the PC users can use native backup tools that the clients are familiar with.

Going with a VPS gives you full control, n-way mirroring , n-way synching, verifiable encryption (encrypt before you send and store on an alien server) etc.
The server can also be used for mail/web/ftp/torrent purposes.

The down side ? 50CHF a month instead of 5CHF a month.

How much is your data worth ? Google VPS and Europe and take your pick.