The economic and social impact of poor air quality in towns and cities is increasingly being recognised, together with the need for effective ways of creating awareness of real-time air quality levels and their impact on human health. With local authority maintained monitoring stations being geographically sparse and the resultant datasets also featuring missing labels, computational data-driven mechanisms are needed to address the data sparsity challenge. In this paper, we propose a machine learning-based method to accurately predict the Air Quality Index (AQI), using environmental monitoring data together with meteorological measurements. To do so, we develop an air quality estimation framework that implements a neural network that is enhanced with a novel Non-linear Autoregressive neural network with exogenous input (NARX), especially designed for time series prediction. The framework is applied to a case study featuring different monitoring sites in London, with comparisons against other standard machine-learning based predictive algorithms showing the feasibility and robust performance of the proposed method for different kinds of areas within an urban region.