For decades, polymers have offered a unique combination of low cost and high durability, and are the material of choice for a huge range of applications. In the current energy system, such polymers require the combustion of fossil resources to provide process heat and electricity for manufacture, and release emissions from embodied resources when incinerated. Polymers which are biodegradable or based on biological feedstock avoid some of this resource use, but in some cases have greater energy requirements than fossil polymer equivalents. This work compares life cycle greenhouse gas emissions for pairs of fossil- and biologically-based polymers under various UK electricity, heat and end-of-life treatment scenarios between 2019 and 2040. As specific emissions from electricity and heat supply reduce over the period, life cycle emissions of all polymers fall. Polylactic acid was found to already have lower emissions than polystyrene in most scenarios. Low-density polyethylene was found to have lower emissions than poly(butylene adipate‐co‐terephthalate) in all cases to 2040. Both bio-based high density polyethylene and bio-based polyethylene terephthalate were found to have lower emissions than their fossil equivalents at some point between 2019 and 2040, depending on energy and end-of-life scenarios. Identifying and acting on these crossover points offers a route to significant reductions in the emissions of polymers, and even suggests that polymers with net negative emissions can be manufactured by 2040, offering the possibility of greenhouse gas sequestration through polymers made from agricultural waste.