The Greens have sought to limit appearances by their leader, Natalie Bennett, during the potential leadership debates, only for the move to be blocked by the broadcasters.

Bennett – who wrote an article in the Guardian apologising for her disastrous performance on LBC radio last week – had agreed to “share the responsibility” for representing the party at the debates with Caroline Lucas, MP for Brighton Pavilion.

It is understood that Lucas was keen to get the exposure as she faces a battle to keep her seat, while Bennett is standing in what is widely regarded as an unwinnable seat. The broadcasters, however, told the Greens “a few weeks ago” that it was not possible for different speakers to appear across the debates being proposed by the BBC, Sky, Channel 4 and ITV.

Bennett’s performances in a series of media appearances have raised concerns within her party in recent months. Party sources insisted the requests to the broadcasters should not be seen as a slight against Bennett, a former journalist who once worked for the Guardian. Another small party is understood to have made a similar request.

However, the attempt to limit Bennett’s appearances will raise suspicions that the party is lacking confidence that their leader will improve the party’s chances in May’s general election. In January, Bennett seemed clear that she alone would be representing the party during prospective debates. In response to the suggestion that Lucas would take part in one, Bennett described the debates as “leader debates”.

The Green leader was humiliated last Tuesday during an interview with LBC’s Nick Ferrari, when she experienced what she later described as a “mind blank” and “brain fade”. She struggled to explain how her party would pay for the 500,000 new council homes it is pledging to build, erupting into a coughing fit when pressed. She told Ferrari the cost would be £2.7bn, prompting the presenter to ask: “Five hundred thousand homes – £2.7bn? What are they made of – plywood?”

Party wanted Caroline Lucas to share the debates with Bennett. Photograph: Gareth Fuller/PA

At the launch of the party’s general election campaign at the Royal Society of Arts in London, Bennett was asked whether she was letting her party down with such media performances. Jenny Jones, former deputy London mayor, leapt to the leader’s defence, saying: “She’s not answering that!”

An appearance in January on the BBC’s Daily Politics with Andrew Neil had also provoked heavy criticism.

Bennett thanked Jones for her intervention but acknowledged that the interview had been “excruciating”.

Last night, a Green party spokesman said: “Caroline and Natalie have, of course, spoken about arrangements for the debates previously. Both felt it was right that they share the responsibility, as leader of the party and its MP.

‘The negotiator on behalf of the Green party inquired into that possibility, but was informed several weeks ago that it would not be permitted. That decision has never been challenged. Natalie will take part in the debates and she has Caroline’s absolute support.”

Under proposals from the broadcasters made public last week, David Cameron and Ed Miliband will go head to head in a live TV debate a week before the general election.

The proposed showdown will be screened on 30 April on Sky News and Channel 4, broadcasters said, after drawing lots. The BBC and ITV plan to stage debates involving the Conservatives, Labour, the Lib Dems, Green party, UKIP, the SNP and Plaid Cymru. ITV will host a debate on 2 April and the BBC’s will be on 16 April.

Cameron has yet to confirm whether he will take part in any or all of the debates ahead of the 7 May general election. He has expressed concern at the exclusion of the Democratic Unionist party from the format.