Let's get the bad news out of the way first – there isn't going to be a legally binding global climate treaty for at least three years, even as negotiators from 193 countries gather once again for the annual UN climate change conference, this time in Cancún, Mexico.

A legally binding global treaty remains the holy grail of climate change policy. It was to help achieve such an agreement that the Copenhagen conference last December was hyped into mankind's last chance to save the planet; and, because it failed to do so, why a sense of doom has since descended on climate activists.

But a new global treaty to succeed the first phase of the Kyoto Protocol in 2012 is not even on the agenda for the conference in Cancún. With climate and energy legislation in the US having been abandoned, and with the two largest emerging powers China and India unwilling to make binding commitments of their own, the most Cancún can achieve is to put in place some important building blocks for a new regime – on issues such as adaptation to global warming, stopping deforestation and paying for it all – which will help rebuild trust and show that the UN process is not actually dead.

But the good news is that this doesn't matter. Contrary to widespread assumption, action on climate change is not dependent on a new legally binding international agreement. Countries are already taking action to cut emissions without it – and they will continue to do so whatever the outcome in Cancún. A global treaty remains an important goal. But it turns out we've been looking at it through the wrong end of the telescope.

To understand this we need to recall what actually happened in Copenhagen. A formal UN agreement was not reached. But all the major economies, including the US, China and India (along with smaller countries representing most of the developing world) did come to a political agreement, the Copenhagen Accord, and this had some important commitments in it. It established the goal that global temperature rise should be held within a 2C limit; committed all countries, developed and developing, to reducing their emissions; and committed $30bn in short-term finance to help developing countries, with a goal of $100bn per annum by 2020.

Despite the opprobrium that the accord attracted at the time, over the past year 139 countries (two thirds of the world, covering more than 80% of all emissions) have signed up to it, and more than 70 have entered their domestic emissions reduction commitments into its annexes.

And that's the interesting thing. The non-UN status of the Copenhagen Accord has obscured the fact that all major countries have now committed to taking action on climate. And they did so as a result of Copenhagen – not as a result of the negotiation, but because of the event itself, the creation of a single moment, under a huge diplomatic, NGO and media spotlight, when governments across the world were required to show their commitment.

Well, not all countries. The US is the big exception: following the mid-term elections, climate legislation is now impossible this side of the next presidential election. But that only makes what's happening in the rest of the world more remarkable. Before Copenhagen the assumption was that if the US would not act, nor would anyone else – certainly not the developing countries. But they are, independent of what the US or the EU is doing. The plans to cut emissions growth now being put in place in China, Brazil, India, South Africa, Indonesia and elsewhere are remarkably ambitious – much more ambitious, relative to business as usual, than those of most developed economies.

And these plans are no longer dependent on UN agreement. They are driven by domestic political and economic concerns. Indeed the narrative has shifted now away from climate change per se towards "green growth" and energy security – using action on emissions as a way to bolster economic recovery and prosperity.

So we need to stop thinking that an international agreement under the UN is the prerequisite for global action on climate change. Before Copenhagen it was believed that if only we could get an agreement, then national policies in every country would follow. In reality, the world works the other way round. Countries need to make domestic economic commitments which they believe they can meet – and for which they are politically accountable at home – before they will commit to a treaty.

So does that mean everything is hunky-dory? Can we all go home now? Absolutely not.

First, in many countries these are only plans, and implementation will be difficult. Developing countries will need financial support. So the commitments rich countries made in Copenhagen to "fast start finance" must be honoured, and quickly. And the recent report to the UN Secretary General on how $100bn a year by 2020 can be raised through new sources, such as the taxation of aviation and shipping, needs to be implemented. It is particularly urgent to get money flowing for adaptation, given the crisis now hitting many vulnerable countries, and for forest protection, where every year sees more irreversible loss.

Second, the EU remains a weak link. It's imperative that Europe moves to its 30% emissions cut target by 2020 – we are already at 17% on 1990 levels, so the current 20% target is now exerting very little pull. This should be the priority for UK and European NGOs, in alliance with progressive business, next year.

Third, current global commitments are not enough. The plans in the Copenhagen Accord would see emissions peak by 2020, which is the essential foundation for global action. But as the UN Environment Programme showed last week, to achieve 2C will require much stronger targets, for 2030 and beyond.

And that is why we do still need an international legally binding agreement – and another Copenhagen-like moment to push world governments into stronger ambition. It won't be in the next three years. But that still leaves plenty to do in the meantime – whatever happens in Cancún.