Recent works have shown that Large Language Models (LLMs) can be applied to ground natural language to a wide variety of robot skills. However, in practice, learning multi-task, language-conditioned robotic skills typically requires large-scale data collection and frequent human intervention to reset the environment or help correcting the current policies. In this work, we propose a novel approach to efficiently learn general-purpose language-conditioned robot skills from unstructured, offline and reset-free data in the real world by exploiting a self-supervised visuo-lingual affordance model, which requires annotating as little as 1% of the total data with language. We evaluate our method in extensive experiments both in simulated and real-world robotic tasks, achieving state-of-the-art performance on the challenging CALVIN benchmark and learning over 25 distinct visuomotor manipulation tasks with a single policy in the real world. We find that when paired with LLMs to break down abstract natural language instructions into subgoals via few-shot prompting, our method is capable of completing long-horizon, multi-tier tasks in the real world, while requiring an order of magnitude less data than previous approaches. Code and videos are available at http://hulc2.cs.uni-freiburg.de