This would be "the greenest government ever", David Cameron declared in May – easy words in the first flush of office. The difficult thing is making them true. In the next few weeks the coalition will confront a series of decisions that will tell us if the heady rhetoric of spring is to be fulfilled – or regretted.

At the Department of Energy and Climate Change, the Lib Dem minister, Chris Huhne, has made a good start. He has committed to a strong European emissions target, published an important roadmap of Britain's low-carbon energy choices, and made a foray into international climate diplomacy.

But elsewhere it's been ominously silent: no speeches from Cameron or Nick Clegg on climate or the low-carbon economy; and, more significantly, none from George Osborne or Vince Cable, the business secretary. This is important, because the paradox of climate change policy is that it is not the DECC that really matters. As six years in government made clear to me, it is the Treasury – and to a lesser extent the Department for Business – that counts. (Luckily, I was in the Treasury for three of those years.) Climate policy is part of economic policy, which is the fiefdom of these two departments. And the word in Whitehall is that both have reverted to their traditional, sceptical policy stance.

A significant feature of Gordon Brown's period at No 10 was the way some of the orthodoxies of Treasury economic policy were overturned: public spending was given a Keynesian stimulus; an industrial strategy was put in place, with interventions in key sectors; new taxes were imposed; and all these contributed to a radical new approach in the field of energy and climate change.

But strengthened by the coalition's overriding priority to slash the deficit, Treasury officials are reasserting departmental orthodoxy: sceptical of economic intervention, resistant to new taxation and opposed to new public spending commitments. At Business Labour's low-carbon industrial strategy has been quietly abandoned, illustrated by the much criticised decision to cancel a loan to Sheffield Forgemasters.

These reassertions of traditional positions are critical, because they risk leaving action on climate change as the sole responsibility of the DECC. The experience of the Labour government is that radical policy change needs cross-governmental priority. And that only happens when ministers are willing to override the institutional instincts of their officials.

This was how Labour in the end implemented a far-reaching climate and energy policy. Under Tony Blair, the record was pretty feeble. He was instrumental in putting climate on the international agenda, but never regarded it as an important domestic or economic issue. Only when David Miliband took over as secretary of state for the environment in 2006 and introduced the climate change bill was a major part of the government's programme. And it really took off when Gordon Brown created a new Department of Energy and Climate Change, with Ed Miliband its first secretary of state.

A slew of radical policies followed, from a "low-carbon transition plan" – which gave every department a carbon budget – to the banning of new unabated coal-fired power stations; from incentives to achieve 15% renewable energy to a "low-carbon industrial strategy" supporting green businesses.

The key was not just a dynamic energy and climate change minister. It was having the support of the whole cabinet, from the PM downwards. It was when Brown made a low-carbon economy part of Labour's governing narrative, its central purpose and message, that Treasury orthodoxy was tamed. (It is not generally known that the Stern review on the economics of climate change, which has influenced governments all over the world, was conceived merely as a way of persuading Treasury officials that there was an economic rationale for strong climate action.) Once his civil servants knew that the chancellor supported strong action, they fell into line. In Business, Peter Mandelson pushed his officials into developing an active industrial strategy.

The coalition has, almost without exception, accepted Labour's climate and energy policies. But to make good those commitments, it too will have to ensure the active support of Treasury and business ministers. With neither Osborne nor Cable known for an interest in green issues, the test will come with three decisions in the next few weeks .

The first is on the Green Investment Bank. This is the innovative proposal, accepted by all main parties, for an independent institution to help finance investment in renewables and home energy efficiency. The last Labour budget not only committed to setting up such a bank, but pledged to fund it with £1bn from the sale of public assets – a move explicitly proposed by Alistair Darling, overriding the view of Treasury officials that there was no evidence that public financing was needed.

But under the coalition that commitment has been withdrawn, and a major argument between the DECC and the Treasury is under way on whether the bank will have any significant public funding – without which the bank will be stillborn, as the Tories' own commission on the subject has argued. Its whole point is to leverage private sector finance through public investment, so it will be critical that Huhne can persuade Osborne and Cable to back such funds.

Second, the government must decide on the development of carbon capture and storage technology. Looking to promote a new British industry with the promise of thousands of jobs, Labour committed to provide both public funding for a first demonstration project and the introduction of a small levy on electricity consumers to finance three more. The DECC insists that both are on track. But Whitehall rumour is that the Treasury is seeking both to close down the competition and abandon or delay the levy.

A third plank of the last government's low-carbon industrial strategy is also up for decision: the push to stimulate a British wind-turbine manufacturing sector, with four global firms announcing plans to invest in the UK. These were dependent on improving the facilities of east coast ports where the companies want to site their factories. So the government announced a £60m port development scheme. The coalition has yet to confirm whether this will go ahead; a decision is set for the comprehensive spending review next month.

These tests matter, not just because of the government's green rhetoric, but because its economic strategy is at stake. Investment in low-carbon energy and green businesses will lie at the heart of Britain's economic recovery: reducing the deficit in ways that undermine sustainable growth is simply self-defeating.

The last government knew this. We will soon find out whether Cameron and Clegg do too.