The government has finally handed in its climate homework. Less than a fortnight before hosting the Cop26 climate summit – arguably the most important meeting in human history – the new net zero strategy is supposed to tell us how the UK will go from long-term hand-waving to now-term problem-solving.

There is both a lot in there, and not enough. Until the government’s official advisers give their assessment we won’t know for sure if the plan stands a good chance of achieving legal carbon targets through to 2037. If you want a simple headline for now, I’d offer this: we’re pointing in the right direction, but setting off at a jog. Physics demands we sprint.

A standout element is the push towards heat pumps (super-efficient devices that run on electricity and suck heat from the air) as a substitute for the gas boilers that heat nine out of 10 UK homes. Recent research found that the boilers in UK homes emit more than double the amount of carbon of all gas power stations combined. We’ve been due a national conversation about how to fix this for too long.

Today, let’s start here: the new funding for household heat pumps is welcome but falls well short of what is needed. Although GBP450m sounds like a big number, it will only enable 30,000 installations a year. That needs to become 600,000 annually – at a minimum – in just over six years’ time.

For those who have worked hard on the issue for years, heat pumps dominating front pages feels like a watershed. It will be a bumpy road before we’re all able to heat our homes without heating the planet. But when we do, burning things for warmth – as people have done for millennia – will become a thing of the past. That this will happen in my lifetime is a source of wonder.

Back in 2021, this underpowered salvo on clean heating is still a significant moment, because it starts the next chapter of climate action. The vast majority of the UK’s success in reducing emissions is largely a result of coal falling from 40% to 5% of electricity generation in under a decade. By 2024 this will fall to zero – a historic achievement. Coal is outstandingly dirty, so eliminating it has a huge impact. The problem is you can’t switch it off twice.

Instead we must look elsewhere. That in large part means cars burning petrol and diesel, and boilers burning gas and oil. Therein lives a crucial difference: no one owns a coal-fired power station, while around eight in 10 households have access to a car and almost everyone lives with a boiler. Chapter one of our climate story was set, for most of us, behind the scenes on industrial sites or out in the North Sea. Chapter two is set in your kitchen.

This has some people worried. After all, it’s one thing to run auctions to build offshore windfarms. It is another to convince millions of households to swap their gas boiler for something we only heard of yesterday. Cue Boris Johnson promising last week that “the greenshirts of the boiler police” won’t be knocking down doors to rip out boilers. The rhetoric was dire, but that doesn’t mean there aren’t genuine challenges here. Once millions of people need to be directly involved, complexity, and the chance of conflict, is baked in.

Perhaps counterintuitively, there is no climate culture war in the UK. Recent polling found 71% of people concerned about climate breakdown – putting it above anything else (including Covid) for the first time. Wider evidence shows the public broadly agreeing – across age, education and leave/remain divides – that climate breakdown is real, human-caused and something the government should be dealing with.

However most people, quite understandably, don’t know what is needed to avoid climate catastrophe. Agreeing you want action isn’t the same as agreeing to wish your boiler farewell, even if the former comprises the latter. Nor does it mean you’re ready to use your car less (or even give it up), or think about changing what you eat. To pretend there isn’t a risk to necessarily rapid carbon-cutting would be foolish.

Which brings us back to the government. It published a research paper on “principles for successful behaviour change initiatives” as part of its net zero strategy on Tuesday, before hastily deleting it (though you can still read it here). An administrative echo of Johnson’s “greenshirts” quote, this is a worrying sign of a government running scared of grownup conversations on the biggest issue of all.

No major transformation was ever won by technology or policy alone. Someone always had to cough up the cash to engage the public. Apple didn’t expect the iPhone to sell itself and, as it turns out, governments didn’t expect avoiding climate breakdown to do so either. Three decades ago in Rio – where Cops were born – nearly 200 governments agreed to implement “educational and public awareness programmes on climate change and its effects”. Precious little has happened since.

Carefully designed programmes to actively recruit the public to – and involve us in – the nuts and bolts of the zero carbon transition are no longer negotiable. If delivered alongside climate policies that preserve fairness, this week’s starting gun could herald that necessary sprint into a safer and better world. Without it we’ll be taking our chances.

• Max Wakefield is the director of campaigns for the climate action group Possible