Diane Abbott says she is “quietly optimistic” about her chances of winning the Labour leadership.

Although victory is more or less in the bag for one of the Milibands, polls say she’s popular with Labour members and her recognition factor, due to her TV work, is excellent.

The 56-year-old has a strong gay rights record and is in favour of same-sex marriage and scrapping the blood donation ban for gay men. On the subject of tackling homophobic bullying, she is articulate and enthusiastic.

She says her campaign is difficult because she lacks the funds of the other candidates, especially David Miliband, and claims the effort is being run “on a shoestring”.

Ms Abbott initially struggled to gain the 33 nominations from other MPs to get on to the leadership ballot. Mr Miliband was one of those who lent her a nomination on the last day.

Did she feel patronised by his support?

“Not really. I mean, the real reason i was able to get on the ballot was because John McDonnell stood down. And I got quite a few votes from him. And I got votes from all wings of the party so I don’t feel patronised. Andy Burnham got lent nominations to get on the ballot and nobody said anything about that.”

She says she’s “quietly optimistic” of her chances of winning and points out that in YouGov polls of the public, she comes second behind Ed Miliband.

She has also been popular in hustings, of which there have been around 40 to date.

However, the fact is she’s almost certain to lose. A reputation as a outspoken rebel endears her to some, but she is still forced to defend her decision to send her son to private school after attacking other politicians for doing the same thing, and her ideals sometimes earn her a name as a firebrand of the old-school left.

While the contest is seen as toe-dipping exercise for some of the other candidates, who want to place themselves as a future leader, Ms Abbott won’t say whether she would stand for the leadership again.

She said: “I don’t know. I wouldn’t want to look that far ahead. But what I would say, is that I hope, if I’m not successful, that this is the last leadership challenge with only one woman on the shortlist.”

She says she’s “surprised” that Harriet Harman, the party’s deputy leader, did not join the race, saying she would have made a “good leader of the opposition”.

Ms Abbott has a strong voting record on gay rights, having only lost points in Stonewall’s index of politicians for missing a number of votes. She sees this criticism as “frustrating”, saying that she was present for the crucial votes and spent weeks on the Civil Partnerships Act committee.

She’s supportive of gay marriage and cites her closeness with former London mayor Ken Livingstone as an example. In 2001, he set up a register for gay couples in London to have their relationships recognised.

“It was something I very much supported. And I think, because he did that, and the world didn’t fall in, the Labour government brought in civil partnerships. I was on the committee which scrutinised civil partnerships, so I had to defeat the Tories, because the Tories tried to amend it in all sorts of ways and water it down.

“As far as I’m concerned, you might as well move to gay marriage and I think we will in due course.”

Ms Abbott is aware of Wednesday’s judgment in California, where a judge ruled against the state’s gay marriage ban.

She said: “I just think it’s very sad that Americans are so far behind us. Obviously we haven’t gone all the way to gay marriage but we have got civil partnerships and the Americans haven’t got there yet.”

She is also against blood donation ban on gay men, which prohibits any man who has ever had gay sex from donating blood, regardless of HIV status or risky sexual behaviour.

“I think it’s discrimination. I’m surprised they get away with it under the law because it’s discrimination against people based on their sexual preference.”

Ms Abbott has been the MP for Hackney North and Stoke Newington since 1987, when she became the first black MP to be elected.

I tell her that I know gay men who live in Hackney – her constituency – who are too scared to hold hands with their boyfriends in public for fear of being attacked.

She’s thoughtful and eloquent on this issue, seeing it as a problem perpetuated by men who have a “frail grasp of their own masculinity”.

She says: “I think it’s related to the issue of homophobic bullying [in schools]. In some ways, I think, homophobic bullying is more of an issue now than it was when I was at school. I can’t recall people being bullied for their sexual preferences. Now it’s a very common thing, to be honest, in city areas like this.

“And it’s very oppressive for young men growing up and the way that they use the word gay as a term of abuse. It’s all part and parcel of the same phenomenon. And I think we need to work more in schools, actually, to counter this type of thinking. I think kids, it’s men, who have a very frail grasp of their own masculinity. They feel so threatened and challenged by sexual difference. but we need to challenge it.”

She isn’t afraid to link the issue with certain cultures, citing reggae artists from her parents’ homeland in Jamaica who have “horrible homophobic lyrics”.

She said: “You challenge them and they say, oh no, we don’t have homosexuality here. But I go to Jamaica all the time, and there are gay people like everywhere else. I think it’s interesting why people of certain cultures feel the need to be so radically homophobic and as I say, i think it’s a matter of a very fragile grasp of masculinity.

“We need to challenge it in schools, primary and secondary schools, I think there’s been a tendency in the past of teachers to shrug it off as teasing or bullying, but we need to take a much firmer line. We wouldn’t allow people to be racially abused in schools. If you can deal with it in schools, you’ve got some chance of avoiding the sort of bullying and harassment that goes on in the street now.”

On the issue of religious rights and gay equality, she contends that religious objections to issues such as civil partnerships and gay marriage are generally a “cover for homophobia”.

She said: “I was opposed to allowing adoption agencies to get state funding that wanted to discriminate against gay couples, Catholic adoption agencies. I was very opposed to this registrar in Islington [Lillian Ladele] who said that her religion didn’t allow her to marry gay couples, and I just think people are using religion as a cover for their homophobia and it’s just wrong.

“You have to distinguish between people’s right to believe something and to practice their religion and the point at which they interact with the public. You cannot use religion as an excuse for discrimination.”

Labour’s members will vote on who should lead the party at September’s conference. Why should LGBT members back her?

“Because I’ve had a longer history campaigning for gay rights than any of the other candidates. I mean, back in the eighties, as a young activist, I was going to Labour party conferences and raising the issue of equality at a time when it was a very unpopular thing to do, to talk about gay rights. It was unpopular to talk about female equality. I’ve been out there and fought, been to the campaigns, wore the t-shirt. The others, in a way, are supportive of gay rights in a much more friendly climate. In the eighties, that was quite a hard thing to do. Particularly in my own community.”

We move on to the issue of diversity in parliament. Earlier this year, the Liberal Democrat MP David Laws resigned from the cabinet after it was revealed he had broken Commons rules by using expenses to pay rent to his male partner. He claimed he had wanted to keep his homosexuality secret.

Ms Abbott says she knows of gay MPs who hide their sexuality from the public and adds that she believes that being an out gay politician is possibly “still an issue” in the Conservative party and Liberal Democrat parties.

She said: “I think there is a notion, a stereotype of an MP, which is a guy in a suit, with a wife and 2.4 children and some parts of Westminster and parts outside London, fall prey to it. You’ve got to remember that a lot of activists in the Tory party and the Lib Dems are actually older. So there is that stereotypical thing. But I think it’s breaking down tremendously.

“I felt very sorry for David Laws, I didn’t feel sorry for what he was trying to do, economically, but I feel sorry that he had to hide his sexuality for so long.”

She added: “I don’t think you should be forcing people to come out because, well, especially slightly older people, they’ve made their choice.

“I think we’ve to concentrate on making it an atmosphere where it’s much more comfortable for people to come out. I think forcing people to come out of the closet isn’t fair on them. But of course the obvious exceptions are people who are voting for homophobic laws and that’s different.”

On the Conservatives’ support for gay rights, she says: “They’ve grasped – belatedly – that the country had left them behind. There is a distaste in middle England for the anti-gay, anti-single parent, anti-black rhetoric because I think we just live in a more diverse society.

“The old Tory position is just not tenable. I think it’s kind of skin deep but credit where credit is due, they have got out gay ministers, out gay MPs, they’ve got black MPs for the first time. It was a kind of a makeover but I’d rather they did that than stayed where they were.”

Ms Abbott sums up her strongest beliefs as “equality, economic equality and civil liberties”.

She added: “One of the terrible things Labour did was to abandon civil liberties to the Tories. You’ve now got Tories calling for repeal of anti-terrorism legislation.”

She blames Labour’ failure to win the election on three things: the lengthy rule of three terms in power, the credit crunch (“people blamed the government”), the expenses scandal, which she says caused disillusionment with the political classes and “the feeling that Labour no longer spoke for” ordinary people.

Much has been made of the candidates’ proximity to former prime ministers Tony Blair and Gordon Brown. David Miliband and Andy Burnham are seen as Blairite, while Ed Miliband and Ed Balls are seen as being closer to Brown.

Ms Abbott is setting out her stall as neither of the two and says the Labour party needs a candidate with no connection with either former leader.

She says: “It [the party] has to leave behind the Blair/Brown years. You need to elect a leader who’s got no connection with the Blair/Brown years and that’s me. It has to start standing for something again. It has to start believing in something again.”

She cites housing, jobs and “misplaced anxiety” over immigrants as key issues Labour must address.

I ask what is the single issue she most wants to achieve in her career as a politician. As politicians tend to do, she gives two answers. As a backbench MP, she wants to bring the Underground to Hackney.

But as a would-be prime minister, she cites leading an “opposition to homophobic policies around the world”.

Not wishing to be cynical, but she is speaking to a gay publication. Surely there are issues closer to her heart, such as eradicating poverty or ensuring that all schools are up to a standard good enough for her own child?

She says: “I think it’s something that as a black woman, as the prime minister for the UK, I would be uniquely able to do. Particularly in those countries that form the Commonwealth countries, like Jamaica, and parts of Africa. So I think as a black politician, I would be uniquely situated to do it. I think it would be important to do.”

I ask her to sum up why she should be Labour’s leader: “I’m the best communicator. The only candidate who knows the party back to front. I was a councillor, a trade union official, I served on the National Executive. I’m the grass roots candidate. I’m the best person to revitalise the party.”