I asked my sister, who is a nurse about this shortly after arriving in the UK and getting sick. In the US I had never been warned not to drink whilst on antibiotics, but in the UK you always get warned and people constantly talk about how they can't drink as they are on a course of meds.
My sister said that it really is specific to the actual antibiotic - some CANNOT be mixed, while others can without any ill effects. My sister seemed to think that it was probably just UK Drs being extra cautious about the ones that do have serious side effects and making blanket statements. If you really want to drink, I would try and find a Merck manual or something like that and look up the specific drug you are on and see what the manual says.
I personally have never had any issues, but as a previous poster mentioned, they had abdominal cramps. Better safe than sorry.