A woman used by David Cameron as an example of the effect of racism in Britain has told BuzzFeed News she doesn't think the prime minister really cares about people like her and that Jeremy Corbyn is the politician who can change Britain.

Jorden Berkeley, a graduate of Warwick University in her mid-twenties, was highlighted in the prime minister's speech at the Conservative party conference in Manchester to explain why he wanted to make his party pledge to push for greater equality.

Cameron told Tory activists: "Do you know that in our country today, even if they have exactly the same qualifications, people with white-sounding names are nearly twice as likely to get call backs for jobs than people with ethnic-sounding names?

"One young black girl had to change her name to Elizabeth before she got any calls to interviews."

But Berkeley, a co-founder of Young Black Grads whose story of discrimination was covered by the media in 2012, said she didn't believe that the Conservatives are on the side of people like her.

"I can only talk for myself but when he speaks, I don't think he's talking to me," she said. "I think that's true for a lot of people my age and people in my community."

She added Corbyn has got her "full throttle" backing and believes it is the new Labour leader, rather than the prime minister, who can inspire societal change that will help people like her.

"I think if anyone is going to inspire change, it's going to be [Corbyn]," she said. "With his position and his views on certain aspects, if anyone is going to make a change, it's going to be Jeremy."

However, she did see it as a positive that her story was mentioned. "It's step in the right direction and it shows that they're willing to tackle it head-on," she said. "But it would take a society overall to eradicate discrimination and that's not on their agenda."

Asked if she thinks the Conservatives have done enough on tackling job discrimination, Berkley said the issue isn't "on the government's agenda". She voted Labour in the general election, but she's considering backing "anyone else" other the Tories.

Berkley also said the story wasn't quite as told by Cameron – she didn't actually drop her name from job applications but instead added her middle name, Elizabeth.

"It's great that he highlighted it but there are better stories," Berkeley said.

"It feels a little bit lazy [that they didn't check my story], because I'm sure if they just asked the question on social media, 'Has anyone has anything happened to them?', responses would have come flooding in, because it's not uncommon."

She said Cameron should consider enforcing blind applications, so employers only saw qualifications at the first stage and could not discriminate on the basis on the basis of names.

"There are people who have had to change their name completely [to get a job]," she added.