Yes you can swap companies. Edf is one of the very expensive ones. Other companies that do support e10 tarriffs are:
Our power energy, ovo energy, I supply energy, so energy, green energy uk, good energy, M&S energy, octopus energy, together energy. If you go into menu on this website you can see price from e10 suppliers for your region. Check those prices and ring the s with good prices. Make sure to confirm that they give 10 hours of off peak electricity not 7 hours like in E7 or that could be another option for you.