Unified speech recognition aims to perform auditory, visual, and audiovisual speech recognition within a single model framework. While speech foundation models (SFMs) have demonstrated remarkable performance in auditory tasks, their adaptation to multimodal scenarios remains underexplored. This paper presents UASR-LLM, a novel framework that adapts frozen SFMs to unified VSR, ASR, and AVSR tasks by leveraging large language models (LLMs) as text decoders. Our approach introduces visual representations into multiple SFM layers through visual injection modules, enabling multimodal input processing and unified hidden representations. The augmented SFMs connect with decoder-only LLMs via a feed-forward adaptor, where concatenated representations and instruction prompts guide speech transcription. We implement a twostage training strategy: visual injection pretraining followed by speech recognition finetuning. SFM parameters remain frozen throughout training, with only visual injection modules optimized initially, and LLMs finetuned using LoRA parameters subsequently. Experimental results demonstrate superior performance over state-of-the-art baselines across VSR, ASR, and AVSR tasks under both clean and noisy conditions. Ablation studies confirm generalization across various SFMs and LLMs, validating the proposed training strategy.