As the dust settles at the end of the UN climate talks, it feels as if we are entering a new phase in the fight against climate change.

The UN process has been resuscitated by the outcome of the Cancún summit. Before the curtain went up in Mexico, climate sceptics in the UK said they could hear the sound of the death rattle for the United Nations Framework Convention on Climate Change process (UNFCCC).

With the agreement of a new and fair Climate Fund, however, we can now start feeling optimistic that we have turned a corner since the disappointment of Copenhagen last year. Rich countries did agree in Copenhagen to deliver $100bn per year by 2020, and next year crucial decisions on how to raise this money must be made. This will then be channelled through the new fund to help poor countries adapt to the impacts of climate change and develop in a low-carbon way.

Companies and investors have recognised for some time now, however, that the private sector has a critical role to play in complementing government action, by climate-proofing their activities and helping to make the global transition to a low-carbon economy. This was underlined at the Copenhagen summit, where both were pushing hard for the elusive global deal that they hoped would set out a clear framework under which businesses could operate.

Company directors are paid to have their eye on the bottom line and many see that strong political action across the world on climate change could spark business opportunities, while possibly creating more jobs and reducing unemployment.

It is in their interests – as well as our own – to recognise the business potential in climate-resilient, low-carbon growth. Europe's environmental sector already employs 3.4 million people and accounts for 2.2 per cent of GDP.

In the United States, a new Oxfam report estimates that two million Americans are employed in sectors, such as water management, agriculture, insurance and disaster preparedness, that help build resilience to the effects of climate change. If new openings are not seized on, Europe risks falling behind the likes of China and the US – both poised to profit from huge investment in low-carbon technologies.

In Cancún, several company directors unveiled practical schemes to underscore their green intentions. For example, the Paris-based Consumer Goods Forum, representing hundreds of manufacturing and retail firms, including Unilever and Tesco, announced that its members plan to use their collective resources to help achieve net zero deforestation by 2020.

This and other initiatives need closer scrutiny before we know what impact they will have on the ground, but it seems to me that this could be more than just greenwashing. I'm expecting there's far more to it than that. Christiana Figueres, executive secretary of the UNFCCC, has recognised that closer partnership between the private and public sectors could offer a win-win situation.

I am heartened by this. We need every tool in the box if we are to help ordinary people cope with the damaging impacts of climate change in many of the countries where Oxfam works, including Bangladesh, Ethiopia and Mexico itself.

Of course, things are not going to change overnight. Many businesses, particularly in the carbon-intensive industries, are clinging to their old ways. They regularly lobby in Brussels to block the EU from making more ambitious cuts to its greenhouse-gas emissions, from 20 per cent to 30 per cent below 1990 levels by 2020.

While they raise concerns about the competitiveness of their industries under stronger European climate action, it would be good to see these companies lobbying to raise the bar in other national capitals, rather than blocking stronger action at home.

The risk of company greenwashing was highlighted by the recent announcement of the Worst Lobby Awards when, in online voting, the European public sent a clear message that they want to see a major clean-up of the Brussels lobbying scene. The German energy giant RWE and its subsidiary npower scooped first prize for claiming to be green while lobbying to keep coal- and oil-fired power plants open.

It's going to take time to change the practices of all corporates but at Cancún we started to sense that things are moving in the right direction. Companies must now seize the fresh momentum – no one can dispute that a serious commitment by global business to change its practices could have a huge impact on the future of the planet.

There is everything to play for.

Barbara Stocking is the chief executive at Oxfam GB.