Lisa Nandy has castigated Labour under Jeremy Corbyn for falling into the “trap” of allowing Brexit to be framed as a binary culture war, saying the party should have outlined positive, internationalist arguments, including a defence of free movement.

Delivering a speech setting out her approach to international relations if she won the contest to succeed Corbyn, Nandy said Labour also missed chances to try to reunite the country around a softer Brexit following the 2016 referendum.

On other global issues, the Wigan MP condemned Corbyn and his team for limiting their criticism of Russia following the novichok poisoning attack in Salisbury and other issues.

She said: “When we chose to show solidarity with Putin rather than the Russian people we completely and utterly failed to live up to our values, and I never want to see us do that again.”

Setting out the case for Labour to devise an alternative framework for global relationships after Brexit, Nandy argued also for an ethical underpinning, including military intervention when needed, and a focus on the climate emergency.

She said Labour should refuse to agree to any trade deal with a country that has not ratified the Paris agreement. That position would rule out a deal with the US under Donald Trump, who is moving to extract his country from the global climate deal.

Nandy, who is among five candidates to make it to the next round of the Labour leadership contest, having won the support of 31 of the party’s MPs and MEPs, is a backbencher. She left Corbyn’s shadow cabinet after the 2016 referendum, amid a series of resignations. She later played a key role in seeking to persuade Labour MPs to try to back some softer variant of Brexit, and has pitched herself in the leadership contest as the person best able to reconnect the party to its former heartlands.

During an interview with the BBC later in the evening Nandy stressed the need for Labour to reach voters in London and in the rest of the UK.

She told the broadcaster Andrew Neil that many of those who had abandoned the party over Brexit at the last election were not irreconcilable with the principle of freedom of movement. Nandy said those voters were supportive of people moving to the UK to work for the NHS but had grown resentful because they felt routes to similar jobs were being blocked. She cited scrapped bursaries for student nurses as an example.

Nandy also committed to implementing any recommendations from the Equality and Human Rights Commission, following its investigation into antisemitism within the Labour party, telling Neil she would suspend any member accused of such attitudes, before launching an investigation.

She also defended her record on Brexit, saying she had voted against Theresa May’s withdrawal agreement, but that she would have supported a deal allowing parliament a role in the next stage of negotiations to avoid a no-deal Brexit. Now that Boris Johnson had secured a majority, she said, Labour no longer had the “means to decide”.

In her speech in London earlier in the day, she said the EU remain side, which she supported, had gone into the referendum without “a story about our place in the world”. She added: “Leave campaigners said we were a small nation with a proud history of punching above our weight. Remain campaigners said we’ll cut your mobile phone roaming charges.”

In the years since, she said, Labour had allowed the Conservatives to frame the Brexit debate around “a series of false binaries”. She said: “You can either be for your country or for the world. And senior Labour politicians rushed headlong into it. It was a serious failure of leadership.”

Labour had missed the chance to try to unite voters behind a consensus view of Brexit, one involving a soft departure based on close trade deals and continued free movement of people. she said.

“We should have been bold enough to defend free movement, and the opportunities and benefits that it brings. But this would have required recognising it has flaws, and not dismissing concerns abut the operation of free movements as simply racist anti-immigrant sentiment.

“We should acknowledge that over decades governments have used the steady influx of skilled labour to cover up a lack of investment in skills and training in the UK, and we should address this.”

With internationalism on the retreat, and the right, under people such as Trump, making “a retreat into narrow nationalism”, Nandy said, it was vital for Labour to make the case for creating new ties.

“It is easy to blame Trump as a single destabilising force. But the UK should not rest on this as an excuse for lack of action on a global level.”