Structure-property relationships in binary polyethylene blends, and how they relate to electrical strength, have been investigated by various analytical steps. Scanning and transmission electron microscopy have been used to characterise in detail the microstructure of blends composed of linear (LPE) and branched (BPE) polyethylene, these have shown a general increase in the size of isothermally crystallised spherulites with increasing LPE content. On increasing the crystallisation temperature, spherulites became more compact and better separated, whereas on quenching, a morphology essentially independent of LPE content was obtained. Differential scanning calorimetry revealed a two phase system whose composition did not depend on LPE content. Electrical testing using an AC ramped voltage, between parallel ball bearing electrodes, was employed to characterise the electrical insulation strength of the materials. Morphological, rather than molecular factors, were found to be key at influencing the electrical strength. Electrical strength was also found to be highly sensitive to the testing procedure and sample geometry employed. From computer simulations it was found that the general patterns of tree growth depended on sample geometry, test conditions, and morphology, in a similar way to that found by experiment. The idea of dielectric failure due to a propagating damage structure is not inconsistent with the simulated or experimental data. A variety of blend systems were also subjected to mechanical tensile deformation and it was found that the morphology was affected significantly, even for small deformations within the elastic limit. Consequently, the electrical strength was reduced by mechanical tensile strain. A 16% increase in electrical strength over BPE alone, could be achieved by the use of a carefully formulated blend, which has potential for commercial exploitation.