Accurate classification of peripheral blood cells is fundamental to diagnosing haematological diseases, including leukemia, anemia, malaria, and thrombocytopenia. Traditional WBC analysis involved sample collection, blood smear preparation and digitization, with analysis then carried out manually. Conventional microscopic analysis was labour-intensive and subjective, and expert dependencies led to the adoption of computer-aided diagnosis systems. Recently, deep learning (DL) approaches were adopted for WBC classification. However, DL models typically rely on large-scale annotated datasets. In clinical settings, acquiring such data is often expensive and time-consuming, leading to a scarcity of expert-annotated blood cell images and significant class imbalances across cell types. To address these challenges, we propose a Few-shot Prototypical Network with a lightweight MobileNetV3-Small backbone, trained under an episodic paradigm that enables generalization from limited labeled instances. The proposed model is evaluated on two WBC classification datasets, namely Peripheral Blood Cell (PBC) eight-class and Raabin-WBC five-class. The MobileNetV3-Small ImageNet-pretrained backbone produces image embeddings, which are later used to compute class prototypes, with query images classified to the nearest prototype by Euclidean distance. Evaluated on PBC (8-way), the model achieves 98.98% accuracy (macro F1: 0.9898; macro-averaged AUC: 0.9998), and for Raabin-WBC (5-way), it achieves 97.50% accuracy (macro F1: 0.9749; AUC: 0.9978). To assess the models' reliability, Grad-CAM and LIME explainability were investigated, and analysis indicates that in-distribution decisions are grounded in morphologically relevant features, including nucleus shape and cytoplasmic granularity. These results demonstrate that lightweight few-shot models can achieve strong, clinically interpretable performance using only a limited number of instances of the labelled data required by conventional approaches, while highlighting domain shift as an open challenge for real-world clinical deployment.