The Tory party has recovered self-belief and has learned how to hope. In Birmingham, the faithful enjoyed themselves, and optimism is important. It fuels enthusiasm, plus the willingness to roll up sleeves and get stuck in to politics at local level. All vital, but even so, the party faces a mighty electoral challenge and there is almost certain to be some early disappointment, in the next opinion polls. At this stage, the most that can be hoped for is to move past Reform into second place, and to regain the ground that was lost in 2024.

In order to advance further, Kemi Badenoch faces two related challenges: to see off Reform and to regain public trust. Reform first, and here it is necessary to brush aside a naive illusion. There are Tories who think that it would be possible to do a deal with Reform. After all, the policy differences are not that great, and the combined opinion poll percentage would be enough for victory.

Yet it cannot be. The mechanics of any deal are impossible. It is hard to know what is going on in Nigel Farage's mind. Although he is obviously a deeper thinker than Robert Jenrick or Suella Braverman, that will not carry him very far. He has lost momentum and we await the verdict on the inquiry into the £5 million. There have been suggestions that he is losing his appetite for politics. In the words of the late Alan Watkins, it is a rough old trade and also an exhausting one.

That said, some of his friends insist that he is still ready for the fray: still thinking in terms of Ten Downing Street, still uninterested in any pact except a Tory surrender. We shall see.

This brings us to the crucial point. Though Nigel may be up for it, are enough voters still up for him? He is a good communicator, but Prime Minister? He may have enough moral and intellectual depth to keep everyone amused over a G and T at the bar of a suburban golf club. Is that really enough?

It may be that enough voters are so disillusioned with the current party system that they will refuse to listen to the denigrators. Say what you like about Farage, they will reply: he can't be any worse than the rest of them. We might as well give him a go. If Nigel does want a political future, he will depend on the 'might as well' vote.

That is what Kemi Badenoch must counter, along with the distrust factor. By 2024, a lot of natural Tory voters were feeling that their party had let them down. They had a point. Mistakes were made, on immigration, welfare and net zero, with Boris Johnson mainly to blame, especially on immigration. There was also the seven-week irrelevance of Liz Truss. She did no lasting damage to the economy - unlike Rachel Reeves. But her non-existent legacy still provides Labour with ammunition. Equally, and this was also true of Messrs Blair and Brown, Tory governments were too ready to spend the peace dividend at the expense of the armed forces.

That is in the past. When the next election does come, Labour and Reform will both try to headline their exaggerations about the 14 years while Kemi Badenoch tries to frustrate them. She will not be able to do this by getting into arguments about yesteryear. She needs to focus attention firmly on the future and on her own qualities, so that an increasing number of voters come to believe in her.

This should not be impossible. It seems to me and to growing numbers of those I talk to that she comes across as strong, clever, confident and likeable. This is hardly surprising. So she is. I have heard one doubt expressed. Up against cuddly Andy Burnham, will she not seem too rough and unfeeling? I find that hard to believe. Although there must be some herbivores who regard cuddliness as a crucial quality, they are surely not that numerous. Do many people really want a teddy-bear in No.10? To paraphrase Alan Watkins, it is a rough old world.

Kemi will have to find a way of coping with Eyebrows Andy. It will obviously be harder than it was with poor hapless Sir Stumbler, but she has two advantages which Mrs Thatcher lacked. She has a sense of humour and she has a pleasant voice. Also, if readers will forgive me, a point which I recently made is worth repeating. Kemi Badenoch is more intellectually self-confident than Margaret Thatcher was at this stage of her career.

This gives her a further advantage over Andy Burnham. If he were persuaded by the Treasury and the bond markets to do something sensible, it would be against his own instincts. The opposite is true of her. Commonsense and good sense are at the core of her political being, and that has been refined by serious thinking.

The PM has a further problem. A number of economic commentators now fear that we are heading for a 1976-style fiscal crisis and one which may be too big for the IMF to solve. Let us hope that they are wrong, but even so, we are a long way from the sunlit uplands and from the economic growth which Mr Burnham has correctly identified as vitally important. To a greater extent than anyone since Boris Johnson, Andy Burnham is designed to be a good times Prime Minister. There is only one problem. His economic grasp is even shallower than Boris's. Good times need to be earned by good policies.

Kemi Badenoch has begun to outline those policies and to set about persuading the public that she knows what she is doing. That task will require hard pounding. It will not be a matter of sudden breakthroughs and a dramatic swing in the opinion polls. But this leader is tough enough for hard times: firm enough to win a reluctant respect and to build a gradual conviction in enough voters' minds that she has what it takes: what the country needs.