Language models (LMs) are increasingly applied to robotic navigation; however, existing benchmarks primarily emphasize navigation success rates while paying limited attention to social compliance. Moreover, relying on large-scale LMs can raise efficiency concerns, as their heavy computational overhead leads to slower response times and higher energy consumption, making them impractical for real-time deployment on resource-constrained robotic platforms. In this work, we evaluate the social compliance of GPT-4o and Claude in robotic navigation and propose E-SocialNav, an efficient LM designed for socially compliant navigation. Despite being trained on a relatively small dataset, E-SocialNav consistently outperforms zero-shot baselines in generating socially compliant behaviors. By employing a two-stage training pipeline consisting of supervised fine-tuning followed by direct preference optimization, E-SocialNav achieves strong performance in both text-level semantic similarity to human annotations and action accuracy. The source code is available at https://github.com/Dr-LingXiao/ESocialNav.