Machine learning models typically struggle to swiftly adapt to novel tasks while maintaining proficiency on previously trained tasks. This contrasts starkly with animals, which demonstrate these capabilities easily. The differences between ML models and animals must stem from particular neural architectures and representations for memory and memory-policy interactions. We propose a new task that requires rapid and continual learning, the sequential Morris Water Maze (sWM). Drawing inspiration from biology, we show that 1) a content-addressable heteroassociative memory based on the entorhinal-hippocampal circuit with grid cells that retain knowledge across diverse environments, and 2) a spatially invariant convolutional network architecture for rapid adaptation across unfamiliar environments together perform rapid learning, good generalization, and continual learning without forgetting. Our model simultaneously outperforms ANN baselines from both the continual and few-shot learning contexts. It retains knowledge of past environments while rapidly acquiring the skills to navigate new ones, thereby addressing the seemingly opposing challenges of quick knowledge transfer and sustaining proficiency in previously learned tasks.