Remote sensing Water Body Change Detection (WBCD) aims to detect water body surface changes from bi-temporal images of the same geographic area. Recently, the scarcity of high spatial resolution datasets for WBCD restricts its application in urban and rural regions, which require more accurate positioning. Meanwhile, previous deep learning-based methods fail to comprehensively exploit the spatial semantic and structural information in deep features in the change detection networks. To resolve these concerns, we first propose a new dataset, HSRW-CD, with a spatial resolution higher than 3 meters for WBCD. Specifically, it contains a large number of image pairs, widely covering various water body types. Besides, a Spatial Semantics and Continuity Perception (SSCP) attention module is designed to fully leverage both the spatial semantics and structure of deep features in the WBCD networks, significantly improving the discrimination capability for water body. The proposed SSCP has three components: the Multi-Semantic spatial Attention (MSA), the Structural Relation-aware Global Attention (SRGA), and the Channel-wise Self-Attention (CSA). The MSA enhances the spatial semantics of water body features and provides precise spatial semantic priors for the CSA. Then, the SRGA further extracts spatial structure to learn the spatial continuity of the water body. Finally, the CSA utilizes the spatial semantic and structural priors from the MSA and SRGA to compute the similarity across channels. Specifically designed as a plug-and-play module for water body deep features, the proposed SSCP allows integration into existing WBCD models. Numerous experiments conducted on the proposed HSRW-CD and Water-CD datasets validate the effectiveness and generalization of the SSCP. The code of this work and the HSRW-CD dataset will be accessed at https://github.com/QingMa1/SSCP.