Electricity networks are critical infrastructure, delivering vital energy services. Due to the significant number, variety and distribution of electrical network overhead line assets, energy network operators spend millions annually on inspection and maintenance programmes. Currently, inspection involves acquiring and manually analysing aerial images. This is labour intensive and subjective. Along with costs associated with helicopter or drone operations, data analysis represents a significant financial burden to network operators. We propose an approach to automating assessment of the condition of electrical towers. Importantly, we train machine learning tower classifiers without using condition labels for individual components of interest. Instead, learning is supervised using only condition labels for towers in their entirety. This enables us to use a real-world industry dataset without needing costly additional human labelling of thousands of individual components. Our prototype first detects instances of components in multiple images of each tower, using Mask R-CNN or RetinaNet. It then predicts tower condition ratings using one of two approaches: (i) component instance classifiers trained using class labels transferred from towers to each of their detected component instances, or (ii) multiple instance learning classifiers based on bags of detected instances. Instance or bag class predictions are aggregated to obtain tower condition ratings. Evaluation used a dataset with representative tower images and associated condition ratings covering a range of component types, scenes, environmental conditions, and viewpoints. We report experiments investigating classification of towers based on the condition of their multiple insulator and U-bolt components. Automated visual detection and analysis of U-bolts has not been previously reported. We demonstrate that tower condition classifiers can be trained effectively without labelling the condition of individual components.