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The heads of the UK and French central banks have delivered a stern warning to businesses that fail to act on climate change.

Bank of England governor Mark Carney and France's François Villeroy de Galhau penned an open letter warning that some companies and industries who do not address the issue and adapt will "fail to exist".

The letter, which was co-signed by the Network for Greening the Financial System (NGFS) - a group of central banks created by the Bank of England in 2017, said that extreme weather events caused by climate change "damage infrastructure and private property, negatively affect health, decrease productivity and destroy wealth".

They warn: "Carbon emissions have to decline by 45% from 2010 levels over the next decade in order to reach net zero by 2050. This requires a massive reallocation of capital."

Mr Carney and Mr Villeory de Galhau called on the financial services to "integrate the monitoring of climate-related financial risks into day-to-day supervisory work, financial stability monitoring and board risk management", stressing that central banks must "lead by example".

Importantly the central bankers want a greater collaboration between organisations, sharing information on how they each tackle climate change in order to better inform others.

In a separate report, while supporting the message of Mr Carney and Mr Villeory de Galhau, the NGFS said there needs to be a transitional approach. It said that "while urgent action is desirable, an abrupt transition could also have an impact on financial stability and the economy more broadly".

It added: "The speed and timing of the transition is crucial.

"An orderly scenario, with clear policy signalling, would allow adequate time for existing infrastructure to be replaced and for technological progress to keep energy costs at a reasonable level.

"In contrast, a disorderly, sudden, uncoordinated, unanticipated or discontinuous transition would be disruptive and costly, particularly for those sectors and regions that are more vulnerable to structural change."

The NGFS also called for regulators around the world to develop a classification system to identify which economic activities have a positive impact on the transition to a greener, low-carbon economy.

It said: "We need collective leadership and action across countries and we need to be ambitious.

"The NGFS is the core of the response of central banks and supervisors. But climate change is a global problem, which requires global solutions, in which the whole financial sector has a crucial role to play."

London has this week has faced days of travel disruption as thousands of climate change activists took to the streets as part of the Extinction Rebellion movement.