Labour's Yvette Cooper has failed to rule out another leadership bid, as the former minister urged Jeremy Corbyn to stand down from the top job amid an attempted coup. "I'm not ruling anything out, but I'm not standing here launching any campaign," Cooper told journalists when she was grilled on her own political ambitions.

The former work and pensions secretary ran against Corbyn in Labour's leadership election in 2015, following the party's disastrous general election result and Ed Miliband's resignation. Cooper was only able to attract just over 12% of the vote, while Andy Burnham received 26% and Corbyn secured 58%.

The left-winger has failed to budge despite a string of Labour MPs quitting from his shadow cabinet, in reaction to both the sacking of Hilary Benn as shadow foreign secretary and as protest over the EU referendum result.

Corbyn and Labour campaigned for a Remain vote at the 23 June ballot, but many of the party's heartlands across England and Wales backed a Brexit.

"I got know to know Jeremy well last year and he was always a kind and friendly man," Cooper said. "He won well and he bought more people into our party. He did not lose the referendum, the Prime Minister [David Cameron] lost the referendum that he called.

"But Jeremy did not show he had any of the campaigning zeal that our party needs in a tough fight. He is losing us Labour support across the country, particularly in the towns and the coalfields that built that Labour movement in the first place.

"Jeremy would be letting down Labour voters and communities across the country, who badly need a strong Labour voice right now and who badly need a Labour government, if he drags this out any longer. I hope he does the right thing in the party and stands down swiftly."

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Cooper, speaking at the Centre for European Reform, also called for the creation of a National Commission on Immigration, which would attempt to build a consensus on the issue. The policy area was a top issue in the referendum campaign, with Vote Leave backing an Australian-style points system, and Cameron had promised to reduce net migration levels to "tens of thousands" – three times less the most recent current official figure of 333,000.

IBTimes UK pressed Cooper on the matter, asking the senior Labour MP if she would want net migration levels to Britain reduced. "I've said previously that it would be better, particularly with low-skilled migration into Britain, was lower. That would be better in terms of the labour market and in terms of communities," she replied.

"I've also separately said that we should be doing more to help refugees and also have more graduates coming to our universities as well. So overall, as I've said previously, I think it would be better to have lower net migration because of the issues around low-skilled migration.

"But rather than say 'look here's a simple solution that will fix everything', part of the reason of having the commission on this is to be able to build a consensus around a new framework."

The comments come ahead of a vote from Labour MPs on a motion of no confidence against Corbyn. A spokesman for the Labour leader previously told IBTimes UK: "There will be no resignation of a democratically elected leader with a strong mandate."