Mr Oborne told Channel 4 News that the newspaper “needs to explain to us why its coverage of HSBC has been skewed”.
In an exclusive interview with Jon Snow, he alleged that there was a “pattern… It’s been going on for more than two years, where nothing unfavourable of any substance has been written about HSBC.”
In his resignation letter, Mr Oborne had claimed that the Telegraph’s coverage of the bank was “influenced by advertising.”
In a statement, the Telegraph denied that its coverage of HSBC was influenced by commercial relationships.
A Telegraph spokesperson said: “”Like any other business, we never comment on individual commercial relationships, but our policy is absolutely clear.
“We aim to provide all our commercial partners with a range of advertising solutions, but the distinction between advertising and our award-winning editorial operation has always been fundamental to our business.
“We utterly refute any allegation to the contrary.”
Mr Oborne joined the newspaper in May 2010, a year after the Telegraph released its award-winning coverage of the MPs’ expenses scandal.
He told Channel 4 News: “I felt so proud to write for the Daily Telegraph.”
The Telegraph said: “It is a matter of huge regret that Peter Oborne, for nearly five years a contributor to the Telegraph, should have launched such an astonishing and unfounded attack, full of inaccuracy and innuendo, on his own paper.”