Conditionally automated driving enables drivers to engage in non-driving-related activities, with the responsibility to take over vehicle control upon request. This takeover process increases the risk of collisions, especially when drivers fail to safely complete takeovers within limited time budgets (i.e., the time offered by automation for takeovers). This phenomenon underlines the significance of providing time budgets that sufficiently accommodate drivers' takeover time (i.e., the time required by drivers to resume conscious control of vehicles). Considering that drivers' takeover time varies significantly across scenarios, this study centres on understanding the role of driver perception in takeover time using the Task-Capability Interface (TCI) theory. The TCI theory suggests that drivers adjust their behaviours based on their perceived task demands and driver capabilities. Accordingly, in a driving simulator experiment featuring diverse traffic densities and distractions, we investigated drivers' takeover time while capturing their perceived task demands and capabilities through a takeover-oriented questionnaire based on established instruments. The results show that drivers generally have longer takeover time as their perceived task demand rises, perceived driver capability diminishes, and perceived spare capacity (perceived driver capability minus perceived task demand) decreases. These patterns fluctuate under conditions of low perceived task demand or high perceived driver capability. When both conditions coincide, drivers necessitate a considerably longer time to regain vehicle control. Our findings on takeover time contribute to the development of strategies aimed at predicting drivers' takeover time, optimizing time budgets, fostering human-centred vehicle design, and enhancing the safety of conditionally automated driving.