There are many reasons why the government’s decision to cut the aid budget is dumb. High among them is the failure to see the link between poverty and climate change. If you want to convince people of the need to save the planet, it is a good idea to make sure first that they are not going hungry, have access to running water and can put their children through school.

The link between social justice and the green agenda applies domestically as well. Millions of people in Britain count the pennies each week because they are struggling to get by. Exhorting them to change their lifestyles or pay more to heat their homes is not enough. If the government is to meet its ambitious targets people who are less well-off are going to need plenty of help, but as things stand they are not getting it.

While the prime minister talks a good game on the climate crisis, the reality is that there is a tension between the colossal transformation being promised and the Treasury’s cheese-paring approach to public spending. Cuts to the aid budget and to universal credit are part of the same mindset; it is hard to see how either will assist in the transition to carbon net zero by 2050.

Boris Johnson encapsulated the government’s problem last week when he told MPs that households would find it hard to pay for air source heat pumps to replace gas boilers. “These things cost 10 grand a pop,” Johnson said. “This is a lot of money for ordinary people.”

It certainly is, and yet the prime minister also knows that securing the support of ordinary people is going to be vital if the government is to meet its ambitious climate goals. What’s more, the backdrop to November’s Cop26 summit – at which the UK is seeking tougher commitments from the global community – is of tighter budgets for those who are less well off. It is not just the GBP20 a week cut in universal credit. The rising cost of oil means fuel prices are up 20% on a year ago; jobs will be lost when wage subsidies are finally phased out in September. The TUC reported this week that more than a million children from key worker households are living in poverty.

Simultaneously, the government is looking to save money and speed up the green transition without prompting political pushback from those least able to meet the costs. This is impossible, which is why ministers are now playing for time and emphasising the role technological progress will play.

Yet delaying action is also problematic. The Office for Budget Responsibility (OBR), the government’s spending watchdog, said last week that putting off taking decisive steps until 2030 would lead to a bigger fall in output and higher levels of debt than would be the case with immediate action.

It is easy to see why ministers would prefer to put off difficult decisions until another day. The Conservative party’s newly won supporters in so-called red wall seats are precisely the group of voters most likely to be worried by rising energy bills and transport costs.

An alternative approach, outlined by the Institute for Public Policy Research (IPPR) this week, would be to marry the green agenda with a poverty-reduction agenda. The left of centre thinktank published a report by its environmental justice commission which suggested the public will hold a veto over the netzero process unless it is seen to be fair. Hilary Benn, one of the commission’s co-chairs, summed it up when he said: “People must be at the heart of the UK’s rapid transition to net zero, or else – to put it bluntly – it won’t succeed.” He’s right about that.

The IPPR has a long list of proposals for ensuring voter buy-in – free public transport, a fund to help consumers switch to green products, higher public investment, guaranteed retraining for low-carbon jobs – all of which will sound expensive to a Treasury that is keen to repair the hole in public finances punched by the pandemic. Rishi Sunak’s instinct will be to play hardball when the cost estimates come in for how much the state will need to pay to secure net zero.

In theory, greening the economy fits snugly with the government’s other agenda: levelling up. The OBR says if ministers act now, the investment needed to achieve net zero adds 21% of GDP – or GBP469bn – to the national debt by 2050. That sounds a lot, but it would be spread over 30 years and is less than the increase in the national debt caused by the pandemic. And, of course, far less costly than doing nothing.

Canada has shown what can be done with the tax system to make the net zero transition smoother and fairer. Justin Trudeau’s government introduced a revenue-neutral carbon tax in 2019, with money raised from polluters redistributed back to households to help them meet the cost of higher energy bills. Most households benefit.

It is now little more than three months until the Cop26 meeting, and despite what it says, the government’s net zero strategy does not pass muster. There has been much less urgency than in Germany, France or the US, and no real evidence of a strategy. Over the next eight years, Joe Biden is proposing to spend billions on making the switch to electric vehicles, ensuring infrastructure is more resilient to global heating, and on clean energy and new low-carbon technology. The US has a plan backed with serious money. Not just talk and cuts.

• Larry Elliott is the Guardian’s economics editor