For days his has been a name invoked, a reminder of election-winning ways now lost, a ghostly presence at the cannibalistic feast of the attempted coup against Gordon Brown. Then he was in front of us, just down the road from Westminster at the London School of Economics. It was Tony Blair yesterday afternoon, speaking to a conference about climate change.

Suddenly, we were in a parallel universe where Blair still bestrode the world, dealing with big, global issues. The US boss of Honeywell who spoke after him followed the American practice of addressing him as "Mr Prime Minister".

The trappings of office surrounded him. He arrived in a big black bullet-proof 4x4. He was selectively deaf to the questions from the television crew on the way in. A blond security man with a curly-wired earpiece stood by the side of the stage. There he was, shaking hands with some of the front row and taking his seat on the chat-show set. A red tie. Lightly tanned, a little thinner and noticeably balder than when he took his leave two years ago this month – a clip that was played on the news this week: "That is that; the end." A clip that reminded us not so much how a departing prime minister is done, but how a great communicator could take such a humiliation and turn it into a moment of theatre that brought the House of Commons to a standing ovation. When Gordon goes, it won't be like that.

Download the new Independent Premium app Sharing the full story, not just the headlines

Back at Westminster, there were medieval marquees up on the lawn opposite Parliament yesterday, just as there were when Blair went. Two years ago, the monarchs of the media on their raised platforms were discussing Blair's record and how his successor might do. Yesterday, they were back to speculate about how much longer his successor might hang on.

The former prime minister dealt with the storm raging outside the lecture hall with familiar deftness, knowing he was among friends. The conference was organised by Policy Network, an international centre-left club set up by Blair and Bill Clinton. Victor Dahdaleh, an environmentally-friendly industrialist, introduced him by declaring: "How? That's the question our guest of honour Tony Blair is the man to answer." How? How do you dislodge a sitting prime minister?

Blair knew that was the question hanging in the air. "We're going to give time for questions and answers," he said, pausing significantly. "On the environment and climate change." But he began by thanking Dahdaleh for his generous introduction, in which he spoke of the "punishing job of the premiership", and the audience for its warm applause. "Very kind indeed. You obviously don't remember me."

Indeed not. Many of the plotters in Westminster have forgotten how unpopular Blair had become at the end, and their restless manoeuvring for a third leader in quick succession does suggest that something unspoken is lurking beneath the surface of modern British politics.

Meanwhile, it was a pleasure to listen to someone who can make a speech, engage in the art of persuasion – admittedly with an audience desperate to be persuaded. He still has the confidence he gained gradually during his time at No 10, the pleasing, not-really-self-deprecating, line.

Then it was off into the Blair climate change speech. You know he's done it before, but it still sounded as fresh as an air-freighted mange-tout. And guess what? He's optimistic that a global deal will be done at Copenhagen this December. The best joke: his sunny optimism, in contrast to the rain-spotted despair down the road.

Read John Rentoul's analysis of the reshuffle in the Independent on Sunday tomorrow. His blog is at www.independent.co.uk/jrentoul