Dear Juraj,
Thanks for replying. The module that I'm using is a Velleman VMA304.
It uses the SPI protocol and SD.h library. According to the manufacturer it should be compatible with the Arduino's. Altough it has both a 3.3V and 5V pin, I've been using 5V since this worked with the CardInfo example. ( https://vellemanstore-vellemannv.netdna-ssl.com/downloads/29/vma304_a4v01.pdf )
As for the SD card that I'm using, I have tried a 512MB Kingston, a 128MB Sandisk and 2GB microSD+adapter Lexar.