Let's be plain, and put the main question first: is Theresa May up to being Home Secretary? Bright, able, and loyal - she doesn't brief against colleagues - she was a champion of party members' right to choose their leader and thus became a friend of Conservative Home. She's shrewdly used her wardrobe in general, and shoes in particular, to convey the sense that beneath her cautious manner lies a pacy character. However, she doesn't always project confidence, has no group of supporters in the Commons, and some colleagues claim that she isn't easy to work with. So, then: can May cope with a big job that she's had no preparation for?

We get an early hint from the set-up of our interview. Many Ministers sit down to be quizzed surrounded by a fleet of press officers complete with tape recorders. But there are just four of us in her Home Office room - the Home Secretary, the two interviewers, and a special adviser. This is a sign of trust or assurance or both. She certainly seems more confident, with her leopard-skin print shoes planted squarely beneath a Ministerial desk, in government than in opposition. The pictures on the walls are large, bold, and painted in primary colours. A single picture frame gleams from behind her desk, on which is poised a big bottle of water.

The obligatory introduction takes place. We want to find out early whether or not she believes that she should take on even more - if creating a separate Ministry of Justice was a mistake, and whether, therefore, it should be re-absorbed into the Home Office. Ken Clarke recently indicated that it should be, thereby suggesting himself out of a job. But May's in no rush to take over: "You can end up with it as it is now or, as Ken said, it would work back together, but I think major reorganisation is not something the government’s about to do."

She adds that counter-terrorism's increased the Home Office workload. "I had a cup of tea with Michael Howard after my appointment shortly after I became Home Secretary, and without telling tales out of school, shortly after I became Home Secretary, and he said that when people used to ask him whether he enjoyed it he'd reply that "enjoy" wasn’t quite the right description." She laughs. "But I’m happy to use enjoy." Perhaps this explains her wardrobe for the day: the same jazzy black and red and green number (we think) that she wore for her major Commons statement on control orders, plus those leopard-skin shoes.

She trots through her priorities, the "three pillars" of the Home Office: cutting crime, controlling immigration, improving security. So let's try a comparison. If the Government's education policy succeeds, parents will see signs of success - more academies, more free schools. What will success in controlling immigration look like on the ground? "Well, obviously, given the objective that we have, what I would hope is that people would be able to see that actually we had reduced the numbers of people, the net number of people, coming into the country. People would, presumably, see that, but it’s difficult to say how."

May goes on, rather tentatively, to say that she hopes that "we would see fewer foreign workers being brought in to do jobs, and actually more young people being trained here in the UK" which "depends on Iain Duncan-Smith’s work programme, and all of those other aspects as well." So will there be less pressure on schools, housing, hospitals? "Your question is difficult to answer, in this sense: people on the ground won’t necessarily connect the two, if I can put it like that." But can she pledge a net reduction in immigration? "That is what we are working to."

On cutting crime, she's clearly putting a great deal of faith in the election of police commissioners next spring. But they'll represent very large areas, with which local people don't necessarily identify (such as, say, the Thames Valley). Will voters feel a sense of ownership, and turn out to vote, especially in areas where there are no local elections? "I think that the ability for individuals to be able to feel that they do have a say by going out to vote for, for somebody to be their elected Police Commissioner takes us so much further forward in terms of the relationship and the accountability of the local police."

So will people turn out to vote? "Well, I’m not sitting here saying that I think there’s going to be x percentage points difference in the turnout. I think my job’s to get the legislation through, and then to communicate the message to people about the possibilities it opens up for people in terms of having their say." She's now floating the kind of anti-social behaviour measures previously suggested by Chris Grayling, her predecessor as Shadow Home Secretary. What does she say to media comment that they're gimmicks, summed up by one paper as: behave, or we'll take away your IPOD?

May is consulting, but says that her aim's to ensure that "the police, primarily, have got a small number of effective tools to use against anti-social behaviour that will be easier and quicker to use. She cites the scandalous Fiona Pilkington case an example of the problem that must be tackled. On security, she is, as we know from other enquiries, fully behind the Prime Minister's determintion to grub up the roots of terrorism. "I take a very simple view that a violent extremist at some point previously been an extremist, and by definition is an extremist, so you do need to look at that non-violent extremism."

Enough, for the moment, of the Home Office. Where is she in the debate about the future of the Coalition? She's not a patron of the campaign against AV, so what are her views? "I’m a first-past-the-post person, and always have been." Does she believe the Party should run candidates in every seat at the next election? "Yes." (It's interesting that she doesn't use the "that's my expectation" formulation favoured by some other senior Ministers.) She's no time, then (assuming a "No" vote), for talk of electoral pacts - of Conservatives withdrawing in some seats to allow Liberal Democrats a clear run, and vice-versa?

"The Conservative Party’s always stood in every seat and I think it’s important to us and I’m personally very pleased that we plan - and I see that Sayeeda said something about this recently - to continue to run candidates in Northern Ireland as well." She says that to stop Ministers speculating about pacts "would not be a realistic interpretation of what happens, but I think we’ve been pretty clear about what we want to do as a party, and I think it's right that we would fight as a Conservative Party."

Is the Party still the Nasty Party? "I said it was perceived as the Nasty Party." And is it? "I don’t think that it’s a phrase that people today would apply to the Party. I think that the perception of the Party has changed." When did that happen? "I think there was a lot of work was done Iain - obviously, I made my speech when I was Chairman under Iain as leader - and obviously David did a considerable amount to change the image of the Party, and how people perceive the Party." So why didn't we win the election? "I think it was always a very big ask to take that number of seats in one fell swoop."

"I think that probably in some areas the Labour message about some of the things that they said we were going to do - and which we weren’t going to do - cut through. And that certainly towards the end of the campaign that began to have an impact." She smiles, rather tightly. "I always hoped we’d win outright." She won't be drawn on Lynne Featherstone's criticisms of the X-Factor - the Liberal Democrat MP is her junior Minister - and rejects any suggestion that she should have resigned after the attack on Prince Charles's car.

"I disagree with the analysis that you’ve put about what happened in relation to the student demonstrations and protests and the incident with the Prince of Wales’ car. We’re very clear that we have to separate out the political responsibility from operational responsibility of the police. The police did absolutely the right thing, which was to initiate a review, an urgent review into how they had policed that incident, um, as a result of that they’ve identified some lessons to be learned and changes to be made in the future, um, and those are now being put into place, and I think that’s absolutely the right way to go about it."

And so, finally, to Conservative Home's Quick Tory Questions, crafted to find out what sort of Conservative Theresa May really is. So, then -

Books: Burke’s "Reflections on the Revolution in France" or Louise Bagshawe’s "Desire"?

Home Secretary: "I wouldn’t read either of them, sorry."

Music. Vaughan Williams's "The Lark Ascending or Madonna’s "True Blue"?

Home Secretary: "It’s probably Vaughan Williams - actually, yes."

TV: The BBC's "Upstairs, Downstairs" or Lizzie Cundy’s "WAGs World?".

Home Secretary: "I have not watched WAGs World, I have not watched the BBC’s Upstairs, Downstairs, either. It would be Downton Abbey, I think."

Night out: The Carlton Club or Stringfellows? 

Home Secretary: "Oh come on! I’ve got, I’ve got" - laughter - "objections to Stringfellows as the Minister for Women and Equalities, and I’m afraid the Carlton Club, hmm. My night out would be with my husband, wherever he chose to take me. 

Night in: Tiger-skin pumps or furry mule slippers?

Home Secretary: "Tiger-skin pumps."