Climate change and political polarisation are two of the critical social and political issues of the 21st century. However, their interaction remains understudied. Here, we investigate the online discussion around the UN Conference of The Parties on Climate Change (COP) using social media data from 2014 to 2021. First, we highlight that cross-platform engagement peaked during COP26. Second, focusing on Twitter, we reveal low ideological polarisation between COP20 -COP25, with a large increase in polarisation during COP26. Finally, we show that this is driven by growing rightwing engagement (a 4-fold increase since COP21) and find no evidence of polarisation driven by individuals moving between ideological groups. With future climate action reliant on negotiations at COP27 and onwards, our results highlight the importance of monitoring polarisation in the public climate discourse and how this may impact political action.