Alison Saunders was on a train to Durham when she heard the guilty verdicts in the trial of Max Clifford.

"I always travel in the quiet carriage, so I can't take phonecalls, but I had a text telling me all about it."

The director of public prosecutions is smiling. Did it feel like cause to celebrate?

"Yes and no. It's never great, is it? A guilty verdict means victims have been abused, and for them it's been a long journey. I was pleased they were believed so from that perspective it's a vindication."

Two weeks ago, however, when the jury was sent home the day before Good Friday, it looked as if the sky might be about to fall in on Saunders's head.

Six months earlier she had taken up her job as director of the Crown Prosecution Service's 7,000 taxpayer-funded staff with a pledge to make the organisation more sensitive to victims. Now it looked as if the decision to prosecute a clutch of public figures for sex offences dating back to the 1970s might prove disastrous – for Saunders and the CPS, for everyone who believes convicting rapists matters, but above all for the victims of sex crimes who might be discouraged from reporting them by the spectacle plastered across the media of so many high-profile failures.

Things got even worse when, following his acquittal for rape, Conservative MP and former deputy Commons speaker Nigel Evans attacked the CPS. His trial had been a "very public execution attempt", he said, and likened it to a "witch hunt". He demanded the CPS repay his £130,000 legal fees, suggested a statute of limitations, and complained about the current law, whereby accusers in sex cases – but not defendants – are granted anonymity.

Colleagues sympathised, with at least five MPs joining a chorus of complaints. At Evans's request, Labour home affairs select committee chair Keith Vaz wrote to the CPS Inspectorate asking "whether we need to make changes". Deputy prime minister Nick Clegg agreed there were "questions to answer".

Coming on the back of not-guilty verdicts in the trials of DJ Dave Lee Travis and Coronation Street actors William Roache and Michael Le Vell, Evans' trial was seen by some as proof that police and prosecutors had got carried away. Determined to prove themselves after the scandalous failure to take complaints about Jimmy Savile seriously, they had gone "fishing" for complaints and then "bundled" them together, leading to the multiple charges laid against Travis, Evans and Clifford. Following the evidence given by some witnesses in earlier cases, Lord Macdonald, one of Saunders's predecessors as DPP and now a Liberal Democrat peer, told a newspaper that prosecutors were in danger of treating a series of weak cases as amounting to a strong one.

Sitting in her top-floor office, with a view dominated by the Shard, but stretching from the City of London to Crystal Palace, Saunders dismisses this idea. "We don't think three weak cases make a strong one," she says steadily. "This isn't a new phenomenon. With any type of offending – assault or shoplifting or theft – if there's a series of offences, we'll put them together. If there's a pattern of offending across a period of time, that gives the jury a context."

She will review the Nigel Evans case, as many such high-profile cases are reviewed. Does she expect to be hauled over the coals at her next meeting with Dominic Grieve, her boss and the attorney general?

"No," she says, and laughs for the first time since we began talking. "He understands. The attorney general understands how we make decisions."

As well as the nation's chief prosecutor, Saunders is now head of a big public-sector organisation, and appears to delight in this part of her job. She peppers her conversation with modern management-speak, talks of building "resilience" and "flexibility" in her workforce, is proud of the CPS's e-learning college, of "joint improvement plans" with police, "individual learning accounts" for staff, a new "management development programme" for managers and "victim liaison units" where expertise is shared.

She joined the organisation in 1986, is the first DPP appointed from within the CPS's own ranks, and says her appointment last November was the highlight of her career – alongside the conviction in 2012 of Gary Dobson and David Norris for the murder of Stephen Lawrence, following her decision to prosecute them for a second time. Rightly proud of her own achievements, she also radiates loyalty to her organisation and sees herself as a manifestation of its success. "It's a reflection of where the service is that it has grown one of its own. That's been a real boost, not just for me, but for the whole service."

An expert in cases involving young and vulnerable witnesses, Saunders is now in a position to promote this agenda, and has lobbied police and crime commissioners for more specialist support. "I think women have had, as witnesses and victims, a raw deal," she says. The new focus on female victims, and challenging stereotypes through specialist training in domestic violence cases, is welcome, but "long overdue".

Saunders is not the first female DPP. In the boardroom, where portraits of all former DPPs hang, there is one woman already: Dame Barbara Mills. But she would like progress for women to be part of her legacy "from all sorts of perspectives. I give talks to students about women in the law. That's where I think the CPS is fantastic. We're now over 60% women, we've got a really good reputation."

When she took over the job she said that investing in training her staff was a priority, along with supporting victims. Born in Aberdeen, educated in south London, Saunders does not fit the posh, white, male mould of the legal elite in this country, and clearly wants the CPS to offer an alternative career path for women. But with 28% cuts to the CPS budget, and low scores in a recent staff satisfaction survey, is this likely?

"It's really hard. I'm not going to say it's easy," she says, before listing efficiency savings including reducing London premises from 40 to two. Despite cuts, she says with blue eyes gleaming, performance has improved. There are things – such as getting better service from police forces and more early guilty pleas – that cuts have "helped us to do, forced us to do".

If cuts are so helpful, would she like to see more of them?

"No," she says, and laughs. "I think there will come a time when we can't take any more cuts without sitting down and asking: 'What does a prosecution service do? What can we do?' We haven't reached that point yet. I'm not entirely sure when that point would be."

Some people would say that in the wider legal context, that point is now. This week saw a dramatic stand-off between government and judiciary when Alexander Cameron QC, elder brother of the prime minister, persuaded a judge to stay – or cancel – the trial of five men accused of fraud on grounds that it was impossible for them to secure the legal representation they needed to ensure a fair trial. Yesterday the Financial Conduct Authority, prosecutor of the case, announced it would appeal.

Saunders will be watching, not least because the CPS has three of its own fraud cases in the pipeline. The situation arose because of cuts to legal aid, and the refusal of barristers with the necessary specailist experience to work for fees which have been reduced by 30%.

Does Saunders think barristers should agree to work for less? She won't say. Nor will she say what she thinks of the situation in which justice secretary Chris Grayling will find himself if this week's decision is upheld.

She also refuses to comment on Britain's over-full prisons – "that's a matter for sentencing policy" – though she doesn't get any pleasure from sending criminals there: "If that's what the law says has to happen, then it does. I get satisfaction from bringing cases to court and seeing justice being done."

Saunders' predecessor, Keir Starmer, who was seen as an astute operator politically, is working for Labour on a possible "victims' law" and may stand as an MP. Saunders insists her interest in the victims of crime is not political at all.

"The reason I'm looking at victims is because we have victims who appear every single day. They're the ones who enable us to bring cases before a court, and I think we owe it to them to improve the work we do and ask how we can help."

This includes following up after trials have concluded, and Saunders has written to Max Clifford's victims asking to meet them. She presumably wouldn't meet the witnesses in a failed prosecution, such as those who accused Nigel Evans or Dave Lee Travis of abuse?

"I have," she says quickly, before turning her answer into a generalisation: "Not necessarily the ones in those cases, but I have met victims in other cases where we have not succeeded."

Saunders has the conviction of Roy Whiting for the abduction and murder of eight-year-old Sarah Payne on her CV, and supports media campaigns on criminal justice issues. What did she think of Rebekah Brooks' naming and shaming of paedophiles in the News of the World?

"Some of the campaigns run by papers, not just Rebekah Brooks, but other papers, have been incredibly instrumental in changing things and raising awareness of issues. I know Sarah's law [allowing access to the Sex Offenders Register] was campaigned for, which was a good thing to do. With some issues, FGM [female genital mutilation] for example, the campaigns that papers have run have been really good. The Evening Standard is doing something on asset recovery. I think these campaigns are really important and get issues to a wider audience than we can."

Saunders' decision to bring the UK's first prosecution for FGM against 31-year-old east London doctor, Dhanuson Dharmasena, who is alleged to have committed the crime in the process of stitching a woman's vagina after childbirth, has been criticised as well as praised, because Dharmasena was not responsible for the initial procedure, but Saunders is bullish.

"The circumstances in this case do fit the legislation, otherwise we wouldn't be prosecuting it. We are very keen to make sure that wherever possible we are looking at FGM cases. We've had very few referred to us. We're still in double figures."

She says prevention is "far better" than prosecution, and suggests a new approach to the problem might include "more proactive work by the police – police going to airports when they know there are times of year people go for FGM ceremonies so they can talk to people on the way there or on the way back".

She praises the awareness-raising among teachers championed by the Guardian, which campaigned for education secretary Michael Gove to write to every school.

"There are some people in England and Wales who still don't know about FGM and may not pick up the signs. I think it's much better now, but five or 10 years ago, if you were a teacher, you may not have thought, 'Why is this girl being taken out of school to go to her home country at a particular time of year?' Whereas now I think teachers are very aware, because of the campaigns that are going on, and we have had cases where teachers have contacted police or social services."

Outside her building, the Guardian's photographer asks Saunders to perch on the concrete barrier that divides the cycle lane from other traffic with the dome of St Paul's behind her – just as a picture of the cathedral sits behind the desk in her office.

Good-natured and jokey as she waits for the photographer to set up, Saunders says: "I feel like doing this." She flexes the muscles in both arms, strongman-style.

"You can do that," I say eagerly, for the camera, knowing she won't.

The director of public prosecutions drops her hands, and presses her brightly painted fingernails together in front of her.