Hull inspection is an important task to ensure sustainability of ships. To overcome the challenges of hull structure inspection in an underwater environment in an efficient way, an autonomous system for hull inspection has to be developed. In this paper, a new approach to underwater ship hull inspection is proposed. It aims at developing the basis for an end-to-end autonomous solution. The real-time aspect is an important part of this work, as it allows the operators and inspectors to receive feedback about the inspection as it happens. A reference mission plan is generated and adapted online based on the inspection findings. This is done through the processing of a multibeam forward looking sonar to estimate the pose of the hull relative to the drone. An inspection map is incrementally built in a novel way, incorporating uncertainty estimates to better represent the inspection state, quality, and observation confidence. The proposed methods are experimentally tested in real-time on real ships and demonstrate the applicability to quickly understand what has been done during the inspection.