I had to look up wedge lamps as I am unfamiliar with them. It would seem the bolb holder would have to have been changed, which in turn means some sort of modified connection to the original wiring loom. I would look at the integrity of those connectors first of all.
Sorry I can't help with this sort of electrical fault. Do you know if your lights have been modified from original? I ask because my A3 is also 2007 yet it appears to have tungsten filament lamps.
Carissa.
If the side lights were defective when you bought it, and it was from a dealer, take it back and get him to fix it. Unless MOT rules have changed recently the side lights must work by law.