A job usually involves the application of complementary or synergistic skills to perform the required tasks. Such relationships are implicitly recognised by employers in the skills they demand when recruiting new employees. Here we construct a skills network based on their co-occurrence in a national level data set of 65 million job postings from the UK spanning 2016 to 2022. We then apply multiscale graph-based community detection to obtain data-driven clusters of skills at different levels of resolution that reveal modular groupings of skills across scales. The obtained skill clusters occupy different roles within the skills network: some have broad reach across the network (high closeness centrality) while others have higher levels of within-cluster containment. Yet there is high interconnection across clusters and no skill silos. Furthermore, the skill clusters display varying levels of within-cluster semantic similarity, highlighting the difference between co-occurrence in adverts and intrinsic thematic consistency. The skill clusters are characterised by diverse levels of demand, with clear geographic variation across the UK, broadly reflecting the industrial characteristics of each region, e.g., London is an outlier as an international hub for finance, education and business. Comparison of data from 2016 and 2022 reveals increasing employer demand for a broader range of skills over time, with more adverts featuring skills spanning different clusters. Our analysis also shows that data-driven clusters differ from expert-authored categorisations, suggesting they may capture relationships between skills not immediately apparent in expert assessments.