Abstract The Southern Hemisphere (SH) eddy-driven jet stream has been shown to move poleward in climate models in response to greenhouse gas forcing, but the magnitude of the shift is uncertain. Here we address the fact that the latest Coupled Model Intercomparison Project phase 6 (CMIP6) models simulate, on average, a smaller jet shift in response to an abrupt quadrupling in CO₂ than the predecessor models (Coupled Model Intercomparison Project phase 5 (CMIP5)), despite producing larger global average surface warming. We focus on the response in the first decade when the majority of the long-term jet shift occurs and when the difference between CMIP5 and CMIP6 models emerges. We hypothesise the smaller poleward jet shift is related to the weaker increase in the meridional sea surface temperature (SST) gradient across the southern extratropics in CMIP6 models. We impose the multi-model mean SST patterns alongside a quadrupling in CO₂ in an intermediate complexity general circulation model (IGCM4) and show that many of the regional and seasonal differences in lower tropospheric zonal winds between CMIP5 and CMIP6 models are reproduced by prescribing the SST patterns. The main exception is in austral summer when the imposed SST patterns and CO₂ increase in IGCM4 produce weaker differences in zonal wind response compared to those simulated by CMIP5/6 models. Further IGCM4 experiments that prescribe only SH extratropical SSTs simulate a weaker jet shift for CMIP6 SSTs than for CMIP5, comparable to the full experiment. The results demonstrate that SH SST patterns are an important source of uncertainty for the shift of the midlatitude circulation in response to CO₂ forcing. The study also provides an alternative explanation than was proposed by Curtis et al (2020 Environ. Res. Lett. 15 64011), who suggested model improvements in jet biases could account for the smaller jet shift in CMIP6 models in the extended austral winter season.