He told delegates how the UK has cut carbon emissions more deeply than any similar nation. Then he boasted how the UK was on track to cut them more rapidly than its peers in future too.

And given the UK is only responsible for 1% of the world's total carbon emissions - why, he said, should UK taxpayers be burdened with having to do more?

Both of these claims are contentious but they're also a major distraction from what the UK really should be talking about at a climate summit like COP28.

The first is about what we're actually doing - rather than what we say we'll do.

COP28 is about getting all countries to commit to more ambitious pledges to narrow the colossal gap between how much carbon is going into the atmosphere now and how much has to be cut to prevent dangerous levels of warming.

The UK already has an ambitious pledge - it's why Mr Sunak is boasting.

But the policies we need to deliver on it aren't currently in place. In fact, the the prime minister has made much of "scrapping" green policies that would put too much burden on the poorest.

But despite Mr Sunak's language around net zero recently, that's not a failure of net zero, or the result of a plot by those the prime minister described as "eco zealots" before he left for the summit. It's a political failure to design and fund policies to deliver on those targets.

Then there's the suggestion we're not responsible for much of the world's carbon emissions, therefore we shouldn't do more than our fair share reduce them.

But that ignores a basic fact about the physics of climate change that is embedded in the very framework around which the UN climate talks are based.

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Carbon dioxide hangs around in the atmosphere for a long time. Between 200 to 1000 years by some estimates.

So a country's "share" shouldn't be measured by what they're pumping out now - but on what they emitted over the course of their history.

That gives the UK a moral responsibility to do more than others at a climate summit.

Not to the point of crippling the economy of course (why should today's taxpayers shell out for decisions made by their mutton-chopped ancestors who were blissfully unaware of the impact industrial emissions would have in future), but it should at least mean the UK has a deeper moral obligation than others.

Look, for instance at our colonial history.

In his speech at the opening of this summit the King spoke, without irony, of his concern for commonwealth countries suffering due to climate extremes.

But what he didn't mention was the UK's contribution to that danger.

The UK grew rich - rich enough to adapt to dangerous climate change - in part thanks to emissions generated by its once vast colonial economy.

A recent analysis by Dr Simon Evans and others at Carbon Brief finds that if you take the UK's colonial economy into account it's historical emissions are doubled.

"The UK has a responsibility to lead, not only in terms of cutting its own emissions, but also in helping developing nations respond to climate change," says Dr Evans.

The UK could restore faith among many at this summit disillusioned by Mr Sunak's recent net zero re-set.

And with 12 days of talks left, there's still time to do it.