High‐voltage direct‐current power cables are vital for the efficient transport of electricity derived from renewable sources of energy. The most widely used material for high‐voltage power cable insulation – low‐density polyethylene (LDPE) – is usually crosslinked with peroxides, a process that releases unwanted by‐products. Hence, by‐product‐free crosslinking concepts that mitigate the associated increase in electrical conductivity are in high demand. Click chemistry‐type crosslinking of polyethylene copolymer mixtures that contain glycidyl methacrylate and acrylic acid co‐monomers is a promising alternative, provided that the curing reaction can be controlled. Here, we demonstrate that the rate of the curing reaction can be adjusted by tuning the number of epoxy and carboxyl groups. Both dilution of copolymer mixtures with neat LDPE and the selection of copolymers with a lower co‐monomer content have an equivalent effect on the curing speed. Ternary blends that contain 50 wt% of neat LDPE feature an extended extrusion window of up to 170 °C. Instead, at 200 °C rapid curing is possible, leading to thermosets with a low direct‐current electrical conductivity of about 10−16 S cm−1 at an electric field of 20 kV mm−1 and 70 °C. The conductivity of the blends explored here is comparable to or even lower than values measured for both ultraclean LDPE and a peroxide‐cured commercial crosslinked polyethylene grade. Hence, click chemistry curing represents a promising alternative to radical crosslinking with peroxides. © 2019 Society of Chemical Industry