There is nothing quite like a Tory leadership contest, and I don’t necessarily mean that as a compliment. During the whittling down of the contenders, new alliances are formed at lightening speed; the most ambitious MPs fall over each other in the scramble to join the winning team and to abandon the losers; and the country – oh the country – is invoked endlessly as though it is a poor damsel in distress.

The campaign teams of MPs really get into the process, loving the excitement and the thrill of possibility as old allegiances crumble and individual MPs – so often ignored in settled times – have a say. The shock of the new is exhilarating. David Cameron and George Osborne (who presumably has done three distinct and unrelated deals to keep himself in business) have gone in under two weeks from being the dominant force in British politics to yesterday’s men after a decade in the driving seat.

For the rest of us, looking on at the spectacle, all we can do is try to ask searching questions and give the contenders to replace Cameron maximum scrutiny. What they seek is the key job in the country and enormous amounts of power over the rest of us. Now is not the time to hang back fearing whether or not they will be offended or their aides will exact revenge by refusing to hand out lollipops afterwards. In that spirit, I can well remember the “oh you had better start being nice to Gordon Brown, he’s the coming man” period in 2006-2007. Where’s Brown now? Once again, the last week has proved the eternal adage of my old boss and friend who said in relation to journalists and leading MPs: “Politicians are like buses. There will be another one along in a minute.”

My thoughts so far on the latest contest? As a great admirer of Michael Gove the politician and human being I am still struggling to process what happened last week. I even feel sorry for Boris. Theresa May looks as though she may be unstoppable on the “who do you want in a room negotiating with Angela Merkel?” criterion. But she has slipped up badly in declining to assure the future of those EU migrants who are already here. Her preparedness to use them as bargaining chips looks, as Tim Montgomerie said on Twitter, uncharacteristically cruel.

Liam Fox is a veteran of these contests and is adding in some spice in terms of his observations about the favourites, but it is difficult to see where he will get the numbers from to go forward. Stephen Crabb, the former Welsh Secretary, a moderniser with close links to the Scottish Conservative leader Ruth Davidson, has impressed already, and it looks as though he will produce some interesting thoughts on infrastructure spending, the detail of Brexit and how the ties that bind the UK might be strengthened.

And then there is Andrea Leadsom, the new darling of the Tory Right. Around her are clustered MPs who are full of enthusiasm for her candidacy.

She is obviously energetic, optimistic and talented. Admirably, she has put a great deal of work into helping form a charity – PIPUK –  dedicated to providing therapeutic intervention that help vulnerable babies bond with their mothers.

But, there’s a but. She entered this contest with a great deal to prove and her supporters seem to think she has done this already when she has most certainly not. Fraser Nelson had a good account of her interview by Andrew Marr on Sunday, and I must say the encounter did nothing to quell my concerns. Perhaps she is what she is cracked up to be by her advocates. But it is incumbent on her to prove it pronto, as she wants to be the UK’s Prime Minister. Here are three of my doubts. I put them out there in a spirit of open-minded enquiry:

1) Her unwillingness to rule out a role for UKIP leader Nigel Farage – which at the time of writing she has not done – is deeply troubling. She was pressed on this by Marr and flunked the test. Farage’s rhetoric in the recent campaign was odious, particularly when he said hours after the result that Brexit is a “victory for decent people”, as though Remainers are not decent patriots. He also ordered and stood in front of the vile Breaking Point poster. Leadsom cannot be held responsible for the Faragists of UKIP announcing that she is their preferred candidate, but a potential leader should be quick enough to spot the danger and say she will have nothing to do with Farage or his acolytes. A man who disgraces himself and his country with that disgusting display in the European Parliament the other day, when he postured that virtually none of the EU’s other MEPs had ever had another job (with a cardiac surgeon sitting behind him, and a former army officer nearby), is the last person we want anywhere near what will be delicate negotiations with our neighbours. Leadsom should have said something blunt and straightforward about Farage (Margaret Thatcher would have done), and yet she did not. That makes me deeply uneasy.

2) A central element of the Team Leadsom pitch is that she was a very senior person in the City, which is great. A successful career in business or finance is hardly a condition for suitability, though. David Cameron had no such background, and neither did Thatcher. But it is Leadsom’s team that has chosen to make such an issue of her vast experience, so it is fair to examine the claim and try to present a fair picture. “She got to the top in the City,” said a pro-Leadsom MP to me this weekend. That seems a tall claim, if you know anything about the City. She certainly was head of Financial Institutions for Barclays from 1993-1997 and a director, although there are many directors in most big banks, and the Financial Institutions function (arranging transactions services for clients) while important is not really the front-line in terms of a big bank. It did bring her into contact with Eddie George and his team at the Bank of England in the Barings collapse negotiations, although a great many banks and institutions were called on by the Bank of England that weekend as they tried to get to the bottom of what had happened and to try to arrange a rescue, which they failed to do. She was then head of Corporate Governance and Senior Investment Officer at Investco Perpetual from 1999-2009. We need to hear more about what exactly was involved, rather than broad brush claims from her allies, if they want to keep trumpeting her record in this regard.

3) Leadsom seems, according to the accounts of some sceptical MPs and in her pronouncements, somewhat Panglossian when it comes to managing the risks of Brexit. Those risks undoubtedly exist, in the City and in industry in particular, and it is important that the next PM is a realist. What is needed now is creative thinking about mitigating the downsides (on the potential impact in the City) and taking advantage of the upsides, such as the digital banking revolution that is going to transform finance. Leadsom has interesting thoughts on fintech, I know. But waving away legitimate worries is unserious. The immediate concerns expressed about investment into the UK are legitimate, and longer term the authorities must carefully do a deal with Merkel, the EU and the ECB that does not harm the City too much. Someone who is running on the back of City experience must have the outline of a plan for all this, surely? Let’s hear it soon.

In this frenetic contest, it is important that the leadership contenders are not taken at the estimation of their supporters – who sometimes want a job from the new leader. Leadsom has come from almost nowhere and the Tory Right is flocking to her. The rest of us outside the Tory party need to keep cooler heads and calmly ask questions and assess the answers.