With the stamp duty pledge, the Tories have found their political mojo

Going into her first party conference as leader of the Conservatives, Kemi Badenoch faced two challenges. First, to save her faltering leadership, and second, on her own behalf and that of her party, to begin earning the right to be listened to by the British people.

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On both counts, she acquitted herself well. She is safe, for now – and her surprise announcement that her government would abolish stamp duty was more than sufficiently bold to command public attention.

As with Sir Keir Starmer the previous week, she saw off a nascent leadership challenge and reestablished her authority, albeit contingent on some sign of further progress in next May's rounds of elections in Scotland, Wales, London and local authorities. Whether the country likes it or not, it is still possible that by this time next year it will have a new prime minister and a new leader of the opposition.

Prickly in media interviews, unreliable at Prime Minister's Questions and prone to an inexplicable overconfidence that makes her occasional gaffes even worse, she is a good platform performer, and certainly no worse than her perennial stalker Robert Jenrick, who – with his hand stuck up a full-bottomed legal wig – gave a bizarre impression of a music hall ventriloquist the previous day.

Ms Badenoch's audience heard a little more about her backstory and, despite the constant murmurings, seemed to show her some affection, genuine or not, when she asked them to “stand with me”.

For the Conservatives, a party still reeling from its historic defeat at the general election last year, followed by a further merciless battering by Nigel Farage and Reform UK, it was all anyone could do. In case they had any doubt about the matter, Ms Badenoch told them that people “are still angry with us”.