The structural characterisation of a broad series of commercial branched polyethylenes in both unoriented and uniaxially drawn fibre sample forms is described, using differential scanning calorimetry and X-ray diffraction. The influences on the crystal structure of polyethylene of branch content, type and distribution, and also uniaxial fibre drawing, have been determined. As well as providing a comprehensive analysis of the effect of branching, this paper also forms the basis for two further papers on this series of polyethylenes. These associated papers examine more intricate aspects of the structure of polyethylene: a partially ordered component and the accommodation of the short chain branches within the crystalline structure. To enable direct comparison between all structures, the unoriented samples were prepared under a common set of conditions and the fibre samples were drawn from these unoriented samples. Fibre drawing reduced the three crystal unit cell parameters for most grades and for all grades an increase in crystalline density was seen. The unit cell parameters of the fibre samples spanned broader ranges than the unoriented samples. Regarding branching parameters, for both unoriented and fibre samples, the a and b unit cell parameters increased with branch content, although with considerable scatter. Some of this scatter in the fibre samples was found to be explained by differences in the branch distribution of the grades: for similar branch contents, randomly placed branches generally produced higher unit cell expansions than heterogeneously placed branches. For ethyl and longer branch types, it is generally believed that for a given concentration, there is little if any effect of branch type on the extent of expansion caused. In this study, however, different degrees of expansion were apparent in the longest unit cell parameter (the a parameter) of the fibre samples, where the range of values seen across samples was largest. In these samples, for similar branch contents of ethyl, butyl, isobutyl and hexyl branches, hexyl branches caused the most expansion and ethyl branches the least expansion.