Smart city combines connected services from different disciplines offering a promise of increased efficiency in transport and mobility in urban environment. This has been enabled through many important advancements in fields like machine learning, big data analytics, hardware manufacturing and communication technology. Especially important in this context is big data which is fueling the digital revolution in an increasingly knowledge driven society by offering intelligence solutions for the smart city. In this paper, we discuss the importance of big data analytics and computational intelligence techniques for the problem of taxi traffic modelling, visualisation and prediction. This work provides a comprehensive survey of computational intelligence techniques appropriate for the effective processing and analysis of big data. A brief description of many smart city projects, initiatives and challenges in the UK is also presented. We present a hybrid data modelling approach used for the modelling and prediction of taxi usage. The approach introduces a novel biologically inspired universal generative modelling technique called Hierarchical Spatial-Temporal State Machine (HSTSM). The HSTSM modelling approach incorporates many soft computing techniques including: deep belief networks, auto-encoders, agglomerative hierarchical clustering and temporal sequence processing. A case study for the modelling and prediction of traffic based on taxi movements is described, where HSTSM is used to address the computational challenges arising from analysing and processing large volumes of varied data.