Hello Andrew et al.
If you go to the Fill that Hole web site you can enter your problem directly, or it will take you through to Apple's App Store or Google Play according to which operating system your phone uses. Although I have never used the Phone facility I believe you can add photos of the problem and, using the phones own location system, state precisely where the problem is, so there is no necessity for you to be aware of where you are - quite useful when you are out in the countryside where cyclists in particular frequently come across dangerous potholes. The Web Site or App then determines the relevant Authority and passes on your complaint. As you say far simpler than trying to use using the Council's Web Site.