Despite only being started on Wednesday, the petition has already attracted over 14,000 supporters.
Amanda Drury, who started the campaign, wrote: "Every time Jeremy Corbyn is mentioned in a news report on the BBC he is referred to as 'the left-wing Labour Party leader'.
"In the interest of fairness and un-biased reporting, David Cameron should also be referred to in terms of his place on the political spectrum - the right-wing Prime Minister."
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Drury said the the change in the way the BBC address the political leaders is "small but significant".
One signatory, Antonio Diaz Kouhia, wrote: "BBC has biased news articles, and if you choose to keep calling Corbyn "the left wing party leader" then Cameron should also be called what he is... the right-wing prime minister."
Another, Chris Eyre, said: "I want fair and unbiased reporting from the BBC... Something that is seriously lacking evidenced by Dennis Skinner having to correct a reporter this week about the lack of fact in her report"
Karen Andresen's son Ryan (pictured) had been in the Boy Scouts for more than a decade when he was rejected for its highest honour - The Eagle Award. His scoutmaster refused to approve him for it after finding out Ryan was gay. "It hurts me so much to watch Ryan suffer for being who he is, because to me, he's perfect," Karen wrote in her petition calling for an end to ban on gay youth in the Scouts. "Ryan has worked for nearly 12 years to become an Eagle Scout, and nothing would make him more proud than earning that well-deserved distinction. "I hope that if enough people come together, we can convince my son's troop leaders to help him feel proud of who he is and all he's accomplished." In May 2013, Boy Scouts of America's National Council voted to overturn the ban. In all, 479,734 people signed the petition. (credit:Change.org)
Get Justice for Quinten(02 of10)
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Quinten Douglas Wood, 15, died from complications of pneumonia. But his elder sister Valerie Wood-Harber said Oklahoma child welfare had neglected to act on her fears that he was being neglected by their father. In the weeks before his death, Quinten was being cared for entirely by his brother Cameron. In her petition calling for the state's child welfare services to be investigated, she wrote: "I called Child Welfare Services at least once a day, every single day for 3 weeks. The social worker assigned to the case visited Cameron at school, promising him that she would do a home visit the very next day. Cameron told me that every day he'd hold Quinten and say, 'Just be patient Bubby, Sissy is sending someone to save us.' No one ever came." 502,788 people signed the petition that forced the state to investigate. Social workers assigned to the case were found to be negligent and dismissed. The state later passed the 'Quinten Douglas Wood Act of 2014' that requires child welfare workers take a child's developmental age into account when investigating claims of abuse or neglect. (credit:Change.org)
Stop The Annuity To Former MPs Convicted Of Corruption(03 of10)
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An Italian petition called for an end to the annual payments given to former lawmakers convicted of corruption, including ties to organised crime. In May this year, Italy's chamber of deputies voted to abolish the payments, after 522,991 signed it. (credit:Change.Org)
Give ‘Bully’ A PG-13 Instead Of An R Rating(04 of10)
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Katy Butler, 17, a high school student and bullying victim, from Ann Arbor, Michigan, started a petition calling for the documentary 'Bully' to be given a PG-13 rather than an 'R' rating. Calling on the Motion Picture Association of America (MPAA) to allow the film a wider audience, she wrote: "Because of the R rating, most kids won’t get to see this film. No one under 17 will be allowed to see the movie...I can’t believe the MPAA is blocking millions of teenagers from seeing a movie that could change -- and, in some cases, save -- their lives. "Over 13 million kids will be bullied this year alone. Think of how many of these kids could benefit from seeing this film, especially if it is shown in schools?" 523,462 people agreed. Eventually, so did the MPAA, which granted the PG-13 rating. (credit:ASSOCIATED PRESS)
Oppose Thailand's Blanket Amnesty Bill(05 of10)
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615,103 people opposed Thailand's controversial amnesty bill that would have protected people, including the prime minister's brother, from corruption charges. In November 2013, the country's senate voted the bill down.
'Light The Lantern For Justice!(06 of10)
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622,328 people signed a Turkish petition in defence of senior officials at Fenerbahçe Sports Club, a football club whose management was accused of match-fixing. The petition claimed the case violated "basic legal principles" and called for a retrial, which was eventually ordered. (credit:Change.Org)
Save Beau's Life And Return Him To His Owner With No Fees(07 of10)
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Beau was sentenced to die for killing a duck. He is, we should specify, a dog. But people in Dyersburg, Tennessee were outraged at the decision and that Beau's owner (pictured) was being charged to keep him in his kennels, where he was allowed to visit him ahead of Beau being put down. The Change.org petition to the city's mayor was ultimately signed by 636,067 people. It pleaded: "Beau does not deserve a death sentence - he was just being a dog." City officials eventually reneged on their plans and Beau was returned to his owners.
Release Grand Theft Auto V on PC(08 of10)
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Not every Change.org petition is on a weighty subject - 728,144 people signed a petition to have Grand Theft Auto V released on the PC. The 2013 blockbuster was initially released only on PlayStation 3 and X-Box 360. Eventually, Rockstar Games announced it would release a PC version. (credit:Bloomberg via Getty Images)
Don't Execute Meriam Yehya Ibrahim For Being Christian(09 of10)
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Meriam Yehya Ibrahim, a Christian, faced death for her religion. Under Sudanese law, her marriage to her Christian husband was void. This and her conversion to Christianity meant she was guilty of apostasy, abandonment of religion and adultery. The penalty was to be flogged and executed. She gave birth in prison, awaiting the sentence to be carried out. Malmesbury resident Emily Clarke started a petition calling on Sudan's government to set Meriam free, writing: "People around the world rallied to raise awareness to #bringbackourgirls kidnapped Nigeria, I hope the world will also stand up for Meriam. "The fact that a woman could be sentenced to death for her religious choice, and to flogging for being married to a man of an allegedly different religion is abhorrent." After the petition fuelled the campaign to #saveMeriam, a Sudanese Appeals Court freed her and she left the country. A total of 1,092,281 people signed the petition, the largest ever for one started by someone from the UK. Ms Clarke, 21, told HuffPost UK: "Change.org provided the platform for me to reach out to my networks and ask others to reach out to theirs in support of Meriam Ibrahim. The result of this cascading effect was a loud, international and unified call for change.” (credit:Change.Org)
Prosecute George Zimmerman Over The Death Of Trayvon Martin(10 of10)
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Trayvon Martin, 17, was unarmed when he was shot dead. Two weeks later, Trayvon's parents Sybrina Fulton and Tracy Martin started a Change.org petition calling on Florida's State Attorney to investigate and prosecute George Zimmerman (pictured). It became the fastest-growing in the site's history and more than two million people had signed it when, a month later, Zimmerman was charged with second-degree murder. "We feel less alone knowing that so many people stood with our family during this impossible time," his parents said. Zimmerman was later acquitted of the charge by a jury. (credit:ASSOCIATED PRESS)