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Accurate energy load forecasting is essential for optimising power systems across buildings, cities, and smart grids. Recently, large language models (LLMs) have shown remarkable capability in capturing complex temporal patterns in energy consumption data, outperforming both traditional and deep learning techniques. However, their reliance on detailed smart meter (SM) data poses significant privacy risks, as such fine-grained information is susceptible to inference attacks. To overcome these challenges, we introduce Privacy-Preserving Time-LLM, an innovative forecasting framework that combines LLM architectures with SM data encoded via Differentially Private Bloom Filters (DP-BF). This encoding safe-guards sensitive consumption data while preserving high predictive performance. Designed for secure cloud deployment, the framework reduces privacy risks associated with honest-but-curious service providers. It employs Low-Rank Adaptation (LoRA) for efficient fine-tuning and utilises Rotary Position Embedding (RoPE) to model temporal dependencies without accessing raw time-series inputs. We benchmark our approach against the widely used differentially private training method DP-SGD. Experimental results demonstrate that the Time-LLM trained on DP-BF-Encoded SM data consistently outperforms its DP-SGD counterpart, reducing forecasting error by approximately 29% on average, highlighting an improved balance between privacy and utility. Compared to a state-of-the-art CNN baseline, our method achieves nearly 52% better forecasting accuracy on DP-BF-Encoded data while maintaining up to 99% membership privacy. Moreover, under adversarial attacks, models trained with DP-BF-Encoding show over 80% reduced vulnerability relative to models trained on raw data, significantly enhancing robustness and stability. To the best of our knowledge, this is the first differentially private LLM-based framework for energy load forecasting using DP-BF-Encoding. It opens new possibilities for privacy-preserving analytics in smart grid environments, with extensibility to other time-series applications such as occupancy detection and demand disaggregation.