Ph.D. in UK/Ireland as "Dipl.-Ing." from Germany
In short, yes. If you're talking about the "traditional" 5 year Diplom, it's essentially equivalent to an MSc, which is what most universities require to start a PhD (although some only require a Bachelor's degree). I don't think you need to keep anything in particular in mind when finishing, apart from making sure that you get good grades for your transcript :)

The application procedure wouldn't be any different from other students, although you may have to explain in some detail what your degree is.