“This is going to be a really, really closely fought contest and I genuinely have no idea what the outcome is going to be,” Hilary Benn tells me when we meet.

The terrace of the House of Commons is the location for this typically relaxed Benn comment.

He is unique among the candidates for Deputy Leader I have spoken to, in that he arrived with no entourage.

He exudes a sense of schoolboy excitement that he does not know who will win, as if he was just an interested observer in the race for John Prescott’s job.

Sipping House of Commons mineral water on a sunny June day, we chat amiably about the dozen or so Skype conversations the MP for Leeds Central has undertaken in the pursuit of second in command.

Journalists and senior Brown lieutenants are deep in conversation a few tables away.

Hilary Benn, the bookies favourite in the six-way contest, seems oblivious.

An MP for just eight years, Benn barely scraped together enough nominations to make it onto the list. Some said his father called in old favours to secure his son’s place on the ballot paper.

Whether that is true or not, what is for certain is that Benn junior surprised everyone by coming top of the list of nominations from the Constituency Labour Parties, who have a third of the vote in this contest.

“It took slightly longer than I would have liked, but I always said from the beginning that I was confident I was going to get on the ballot paper, and I did,” he tells me.

Benn declines to explain his appeal to the party grassroots, instead stressing the common theme of all the candidates, the members:

“I think the party wants to be heard and it wants to be listened to. They want a chance to participate in discussions about what we are going to do in the future.

“The contest has been a wonderful process. Genuinely I think the party feels good about it, people have been coming to hustings, discussed a huge range of issues.

“People have been joining the party in large numbers.”

Benn takes a novel approach to the much-discussed renewal process:

“Quite a good way of trying to frame the task we have got is to say, ‘supposing we hadn’t been in government for the last ten years.’

“If we were coming in for the first time now, what would be the priorities? What would a Labour government be seeking to do?

“That is why affordable housing has really come to the fore in these debates.

“I believe in a practical and a purposeful politics, if we are going to overcome cynicism and alienation, which I worry about.

“The best way you do that is when people see politics being relevant to their lives, helping them deal with their problems and realise their dreams and aspirations for the future, as opposed to being remote, distant and alienating.

“I represent a constituency, Leeds Central, where at the last election 54% of the electorate voted for nobody at all.

“Why is that the case? What do the constituencies with the lowest turnout have in common? Poor inner cities.

“Where will you see the highest turnout? Leafy suburbs. Why?

“Because more people in the latter type of constituency see politics as having a connection to their lives.

“The minimum wage and the increase in child benefit, tax credits and paternity leave, all came because of politics.

“They didn’t fall out of the sky one morning because someone was feeling generous.

“We worked very hard to make them happen but it’s about seeing the connection between that.”

One of the problems for Labour is that the public have absorbed the positive changes in British life over the last ten years, and now are asking ‘what else have you got?’

The appeal of David Cameron’s Conservative party has alarmed many Labour MPs, especially those sitting in small majorities.

With the imminent arrival of a Prime Minister representing a Scottish constituency, many commentators are predicting heavy losses for Labour, perhaps even a loss of power.

Benn is predictably upbeat:

“There is everything to play for at the next election. I genuinely do not believe that the British public are at the point where they have decided they have had enough of a Labour government.

“I am relishing the next election because it is going to be a choice between a person of undoubted substance, Gordon Brown, serious politician, serious times, strong moral core, thinks about issues and has shown himself to be radical on a number of things, and David Cameron, who can take his tie off as much as he likes, he can pose for photographs with people … all politics is what do you stand for, what do you believe in, what are your policies.”

At a time when the Conservatives should have been sitting back and watching Labour expose their divisions, the opposition have instead been caught in an unwanted ideological battle over a core Tory policy.

Cameronite Shadow Education Secretary David Willetts gave a clumsy statement on secondary education, backing Blair’s cherished city academies while appearing to drop grammar schools altogether.

Resignations, u-turns and an avalanche of bad headlines followed.

Benn points to this tussle in the Tory ranks as proof that the opposition threat is a mere paper tiger:

“The grammar school debate. Honestly, I look you in the eye and I tell you, I haven’t a clue what their policy is on that subject.

“Now, if I haven’t got a clue, and you may not have a clue, and he hasn’t got a clue, what are the public to make of this?

“It has actually been quite illustrative, because it has demonstrated a lack of clarity about policy in one of the few areas where they were trying to have one, and it demonstrates that the Conservative party, as an entity, isn’t entirely sure that it wants to be taken in all the directions he wants to take it.”

As attacks on David Cameron go, that was pretty mild.

Benn is avuncular and often seen as a ‘soft’ member of the Cabinet, certainly in comparison to John Reid.

He rankles slightly at the suggestion that International Development is an easy Cabinet post, responding that two million people in refugee camps in Darfur and political infighting in Ethiopia is not soft-core politics.

Benn stresses that he served time as a junior minister at the Home Office, a hard enough job even if you aren’t in charge of prisons.

One of the disadvantages of being the son of Tony Benn is that people tend to imagine Hilary as just like his father.

He is, again, avuncular when asked if a famous father is a blessing or a burden:

“In the end I think it kind of evens out. Sometimes it meant that people were more friendly toward me, sometimes people were less favourably inclined towards me, in the end it can only take people so far.

“I am me, he is him, I am incredibly proud of him he has been enormously supportive of me but each of is ourselves.”

I am accused of not being supportive, being one of those feral beasts in the media.

Benn waggles his finger at me as he defends Tony Blair’s astounding assertion that it is the press who are to blame for public cynicism about politics and politicians.

“There is no doubt that the perception of spin has harmed politics in general. That’s why I talk about a more straightforward type of politics. My sense is that there is a type of yearning for that out there.

“Why have we got the problem? Partly down to us as politicians, partly down to you as journalists.

“Let’s put it in very sharp terms. Ask people about their most recent experience of using the NHS. 80% say good, very good or excellent. Ask people what they think of the state of the NHS in general, what answer do you get?”

Benn, 53, was raised in a household where the NHS was just one symbol of the collective power of the Labour movement.

His father was a leading member of the party and Hilary, one of four children, worked as a policy adviser in various trade unions for 22 years.

An unsuccessful Parliamentary candidate in 1983 and 1987 in Ealing, where he was a local councillor, in 1997 he was appointed a special adviser to Education Secretary David Blunkett.

He won a by election in Leeds Central in 1999, and by 2001 he was a junior minister at International Development.

After a short spell at the Home Office, he returned to DFID in May 2003.

Five months later he was appointed Secretary of State for International Development, and in that role he grants aid to countries that criminalise homosexuality.

As a tax-payer, why should I pay money to help Jamaica, for example, where gay people are beaten, abused and murdered?

“We are trying to deal with poverty and part of what we are doing is trying to help them improve their policing.

“In the end, at International Development, I can’t pretend I am going to be the government of all these countries. We might as well tell the truth to eachother.

“You may be in a country where you have a rotten government. Should you be penalised twice over, once because you are poor and once because you have a rotten government?

“I don’t think that is the right approach. Those countries must answer for what they are doing and those societies must try and change in the way that we have made the change.”

Homophobia has become an issue closer to home as well, namely in eastern Europe.

The Polish government repeatedly talk tough on homosexuality, with new laws to ‘protect’ children from gay influence, and the President predicting the end of the world if homosexuals are given equal rights.

These are the people we are in union with. What use is the EU if it cannot guarantee the rights of LGBT people?

“It is not an easy process, and I must say, seeing some of those pictures, and hearing some of those reports of what has gone on is pretty disturbing.

“But, as our society has shown, we have seen a transformation in your lifetime and certainly in mine. We criminalised people when I was born, up until we changed the law.

“I reflect on my own political life, my experience as a councillor in west London in the 1980s.

“Ealing council was by no means the first, there were other pioneers in London, but I remember the first time that we put adverts for teaching jobs in the gay press, saying we welcome applications regardless of sexual orientation.

“Some people were apoplectic.

“I remember about ten years later, I was standing on Turnham Green underground station, waiting for the District Line to arrive, and next to me was this large poster, urging people to join the police force. At the bottom it said ‘we welcome applications from people regardless of sexual orientation.’

“I remember that very moment thinking ‘that is how our society has changed’ and people do get it in the neck for being part of a pioneering process.

“We are profoundly different and profoundly better as a society as a result of that change and that is a combination of legislation, things we are really proud to have put on the statute book, but it is also social attitudes changing.

“Each society has got to make that journey, and politics can be both a powerful force in helping to make the change, and also use legislation as a bookend on social change, helping to solidify it within society.

“It is about each country standing up for the values it represents. It is about offering support to people who are trying to stand up for those values, and leading by example. Those are the things that we can do.”

The votes for Deputy Leader are already in.

On Sunday 24th June, Gordon Brown will be declared leader of the Labour party.

And once all the second preference votes have been cast, and perhaps third preferences as well, the party will have a new deputy.

Bookies, who after all make a living from correct predictions, think it will be Hilary Benn. What is his vision for the job he is tipped to win?

“If this is about party members having a voice, a greater voice in what is being decided, then members want a voice on policy.

“Therefore if you want the Deputy Leader to be in part your voice then he has to be in Cabinet with policy responsibility, on the committees and arguing all of that.

“In the end it is ideas that will bring people back into the party, it is causes, passions, things we haven’t yet done. That is what motivates people to join political parties.”