It is understood that he has decided not to apply for re-election to the post and tendered his resignation at the Virgin Media annual meeting, which took place today.
Connors is one of two Virgin Media board members, along with Edwin Banks, who have previously worked for Huff at his US-based hedge fund operation. He was reported to be considered too close to Huff, who owns 5.7% of Virgin Media, by fellow investor Franklin Mutual Advisers.
Yesterday, Franklin Mutual, which has a 9.45% stake in the cable company, questioned Virgin Media's strategic direction and demanded discussions after last week's poor first-quarter results.
In a filing to the US Securities and Exchange Commission, the investment firm said that it wanted to talk to Virgin Media regarding its "strategic direction, corporate governance and management".
As part of its first-quarter results, Virgin Media said it expected to lose subscribers to its services this quarter after recording a first-quarter increase in paying subscribers of just 36,100, to 3.39m.
The pay-TV cable company blamed the slowdown in subscriber growth on its rival BSkyB's decision to pull Sky News and Sky One from Virgin's subscriber package, and warned that things would get worse.
Virgin Media is due to confront Sky in a legal challenge after filing at the High Court accusing its satellite broadcasting rival of anti-competitive behaviour.
The cable broadcaster alleges that Sky more than doubled the asking price of the rights for Virgin to carry its basic channel package and also threatened to pay nothing to Virgin for its channels, which include Bravo and Living TV.
The loss of the basic package has deprived 3.3m Virgin Media customers of hit shows such as 'Lost' and '24' after Sky removed them from Virgin Media at the end of February.