Flood events cause substantial damage to urban and rural areas. Monitoring water extent during large-scale flooding is crucial in order to identify the area affected and to evaluate damage. During such events, spatial assessments of floodwater may be derived from satellite or airborne sensing platforms. Meanwhile, an increasing availability of smartphones is leading to documentation of flood events directly by individuals, with information shared in real-time using social media. Topographic data, which can be used to determine where floodwater can accumulate, are now often available from national mapping or governmental repositories. In this work, we present and evaluate a method for rapidly estimating flood inundation extent based on a model that fuses remote sensing, social media and topographic data sources. Using geotagged photographs sourced from social media, optical remote sensing and high-resolution terrain mapping, we develop a Bayesian statistical model to estimate the probability of flood inundation through weights-of-evidence analysis. Our experiments were conducted using data collected during the 2014 UK flood event and focus on the Oxford city and surrounding areas. Using the proposed technique, predictions of inundation were evaluated against ground-truth flood extent. The results report on the quantitative accuracy of the multisource mapping process, which obtained area under receiver operating curve values of 0.95 and 0.93 for model fitting and testing, respectively.