With a rapid increase in the ageing population across the globe, there is an urgent need for the development of affordable and sustainable solutions to provide aged care support services. Recent advancements in sensor technologies coupled with the use of artificial intelligence (AI) make it possible to monitor and classify the activities of daily living (ADL) of residents in aged care settings, making it easier to detect and predict any potential health problems. The development of such an architecture, however, presents two key challenges: (i) the determination of appropriate sensors and (ii) the selection of suitable AI approaches to recognise individual activities. While existing studies often only focus on addressing one challenge at a time, in this paper, we present the design and implementation of a real-time human activity recognition system called HARNIC, which uses not only non-intrusive sensors but also utilises continual learning to classify individual activities in a simulated environment. We conducted a thorough analysis of current non-intrusive sensors and subsequently selected appropriate sensors for real-time activity monitoring by considering several features such as adjustable sensitivity, detection range, trigger modes, processing power and accuracy. Using the sensors, we designed and simulated a smart aged care environment in a laboratory setting and collected ADL data. This data is categorised into three levels i.e., low, medium, and high, based on the type of activity. We then worked on generating a benchmark data set used to build machine learning models and performed testing of our models. To address the second challenge, we considered incremental and non-incremental methods and evaluated their effectiveness in recognising individual activities in real-time. Our initial experiment results indicate a clear superiority of our HARNIC over the existing state-of-the-art methods used in this study.