Intelligent systems deployed in the real world suffer from catastrophic forgetting when exposed to a sequence of tasks. Humans, on the other hand, acquire, consolidate, and transfer knowledge between tasks that rarely interfere with the consolidated knowledge. Accompanied by self-regulated neurogenesis, continual learning in the brain is governed by the rich set of neurophysiological processes that harbor different types of knowledge which are then integrated by the conscious processing. Thus, inspired by Global Workspace Theory of conscious information access in the brain, we propose TAMiL, a continual learning method that entails task-attention modules to capture task-specific information from the common representation space. We employ simple, undercomplete autoencoders to create a communication bottleneck between the common representation space and the global workspace, allowing only the task-relevant information to the global workspace, thereby greatly reducing task interference. Experimental results show that our method outperforms state-of-the-art rehearsal-based and dynamic sparse approaches and bridges the gap between fixed capacity and parameter isolation approaches while being scalable. We also show that our method effectively mitigates catastrophic forgetting while being well-calibrated with reduced task-recency bias.