"Every time Jeremy Corbyn is mentioned in a news report on the BBC he is referred to as 'the left wing Labour Party leader'," the petition says.
It adds: "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'".
Support for the "small but significant changes" gained traction on Thursday, having garnered a large number of signatories in just 24 hours.
The BBC defended their journalists choice of words, commenting choice phrases were employed as a matter of "specific editorial justification" to enhance its audience's understanding.
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"Our journalists use descriptions of different political leanings to help the audience’s understanding or where there is a specific editorial justification," a spokesperson told HuffPost UK.
"Mr Corbyn was to the left of the other candidates and now he has been elected it is fair and accurate to say the Labour leadership is more to the left, or more 'left wing' than before.
"We do not use such labels in every instance, but we have taken a similar approach with the different political shades of other parties."