The former Terminator and current governor of California is in London for climate change discussions with the outgoing PM, the environment secretary David Miliband and a selection of business leaders.

Schwarzenegger said that Blair’s visit to the US last year, which included signing a deal between the UK, California and BP, had “been an inspiration to everyone in California” – and had since led to the state adopting a Blair-esque cap-and-trade model on reducing CO2 emissions.

Blair responded by praising Schwarzenegger’s “vision and leadership” on the issue of climate change, specifically referring to California’s role in leading some US states to implement Kyoto-type targets.

Although Schwarzenegger said he would support Blair’s appointment as envoy for the US, EU, UN and Russia for peace in the Middle East – a position the PM is rumoured to be considering – the last action hero had another job in mind.

“Out of selfish reasons I hope that he becomes the envoy for the environment and brings all the countries of the world together to join some kind of treaty – a Kyoto kind of treaty – that everyone can join and we can all together reduce greenhouse gasses,” he said. “I think the Prime Minister is the only person who can do that.”