The Liberal Democrats should consider deposing Nick Clegg as their leader before the next general election, a prominent peer has said.

Lord Oakeshott of Seagrove Bay, a close ally of Vince Cable, said the Lib Dems needed to take a careful look at their "strategy and management" because the party had seen its support halve since the election.

The peer, a persistent Clegg critic, told Radio 4's Today programme: "We have lost over half our market share – if you like to put it that way, if we had been Sainsbury's – since the election. Any business that had done that would be looking very hard now at both its strategy and its management to see how we get some of that back because otherwise we are going to lose a large number of seats at the next election."

The deputy prime minister, who knows that Oakeshott is agitating for him to be replaced by Cable, told the Guardian this week that he would lead his party into the 2015 general election and beyond.

In his interview Clegg said: "I am going to lead this party through the next general election and beyond. But I am acutely aware of how much work we have got to do over the next two and a half years."

Oakeshott made his intervention as part of a discussion on the Today programme with Peter Kellner, the president of the YouGov polling organisation. In a recent poll, published in the latest edition of Prospect magazine, Kellner found three times more respect for Cable than for Clegg among Lib Dem voters. The poll was highlighted in the Guardian by Martin Kettle on Thursday.

Supporters of Cable are highlighting this poll to call for Clegg's removal. The business secretary is not moving against Clegg, though he did indicate in an FT interview earlier in the summer that he would be available if there were a vacancy.

In his Guardian interview Clegg brushed off Cable's remarks. "I have a lot of sympathy for Vince. I have been there myself. You get asked by a journalist would you ever, ever, ever considering standing. I was in exactly the same invidious position when people kept asking me at the time when Ming [Sir Menzies Campbell] was leader. Almost anything you say will get interpreted mischievously. I work very, very closely together with Vince. Just a few days ago we had an hour-long telephone conversation about the state of the British economy and what we want to do together. We have very complementary skills. We work together very well as a team."

But Clegg said he was aware of a poll of party members by the Lib Dem Voice website which found 87% support for Cable compared with 31% for Clegg. The poll found that Clegg was marginally ahead (by 47% to 46%) when members were asked about whether he should lead the party into the next election.

Clegg said: "Of course there are some [party members] who are worried. Of course they are. Who wouldn't be worried? And there are some, bluntly, who don't like what we have done by entering into coalition and don't like the way I have led the party in a fairly controversial way. But the worst thing to do when you are half way up a mountain is to suddenly either jump off a cliff or retrace your steps. I always believe in going forward, not going backwards.

"As long as I have been in politics I have read portentous pieces from commentators and pundits saying the Liberal Democrats are just about to die – tomorrow … if we were not in coalition now I am sure I would be reading pieces saying that because Nick Clegg failed to take the strategic opportunity of being in coalition the Liberal Democrats face irrelevance and extinction. It is the nature of the beast.

"People don't like the fact that Liberal Democrats are an active and important and powerful part of the political scene. We have proved them wrong before and will prove them wrong again. But we've got to do a lot of work to recover our fortunes in the next two and a half years."