A Labour government should consider offering a referendum on the future shape of the monarchy, the Labour leadership hopeful Clive Lewis has argued, as he unveiled a radical policy platform based around proportional representation and working with other parties.

In a speech formally launching his campaign, the Norwich South MP said the crisis over the Duke and Duchess of Sussex’s future showed the need for a reconsideration of the monarchy’s role.

“Why not have a referendum in this country on the future of the royal family? We’re a democracy. I’d rather see us as citizens than as subjects in the 21st century. Let’s talk about what a modern state looks like and what the role of the royal family would be in that,” he said.

The bulk of Lewis’s speech was a call for a radical rethink of Labour’s role and approach following its latest election defeat, which he said showed the party “needs to modernise, or it will die”.

Lewis currently has only four of the required 22 nominations from Labour MPs to reach the next stage of the process to replace Jeremy Corbyn, the fewest among any of the six candidates. The deadline for nominations is Monday.

But asked whether his best hope was another leader adopting some of his ideas, Lewis insisted he was hopeful of progressing, and called for some of the undecided MPs to lend him support to ensure a better mix of ideas in the race.

Without criticising any candidates by name, Lewis warned that frontrunners such as Keir Starmer and Rebecca Long-Bailey would struggle to put in place the necessary radical changes to transform a party which, he noted, had only won eight of the 28 elections over the last century.

“Do I believe that any of the candidates who are standing are so scintillatingly brilliant that they, on their own, with the tweaking of a few policies, are going to be able to undo 100 years of what has already happened? I’m struggling with that concept,” he said.

“People have seen a route map of how they’re going to win. They’ll need this particular section of the Labour electorate to get to the next stage, then this group here, which has this vested interest.

“What you begin to do is you begin to build a cage for yourself, and once if you’ve won – yes, you’ve won, but you’re in that cage.”

Lewis said Labour needed to become less centralised and more collaborative, warning that debate was being stifled by “sectarianism and tribalism”.

“We must come out in favour of proportional representation – not only because it is the fairest way to elect a parliament, but also because it will put into practice our fundamental belief in the value of collaboration and cooperation,” he said.

He also called for the Lords to be replaced with an elected second chamber. “How can the public have faith in politics when people like Zac Goldsmith can lose their seat in a democratic election one week, get put in the House of Lords the week after, and be back in cabinet?”

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Pointing to the long-term decline of traditional leftwing parties in places including France, Germany and Greece, Lewis said a new leader must address “some fundamental issues”, adding: “A few tweaks of policy here, or a slight change of leader there, aren’t going to bring the real change that this country urgently needs.”

“We have to accept that democracy is in crisis, that we face a climate catastrophe, and epoch-defining possibilities and challenges from the tech revolution,” he said in the speech. “We can’t have more of the same. The Labour party needs to modernise, or it will die.”

A commitment to electoral reform was “the litmus test of Labour’s survival”, Lewis said. “A winner-takes-all politics just doesn’t allow us to deal with the complexities of the world as it increasingly is.”

Meanwhile, Starmer will promise on Saturday that his bid to win Labour’s leadership will be focused on defending radicalism, winning trust and becoming relevant.

Ahead of the official launch of his campaign, he said: “We have to rebuild people’s trust in Labour as a force for good and real change. We have to take the fight to the Tories and make the case for how our values and ideas can deliver the change Britain so desperately needs.”

Starmer will be introduced at his campaign launch by Doreen Lawrence at the Mechanics Institute in Manchester, the birthplace of the British Trade Union Congress.

Before the launch, he said: “Labour wins when it glimpses the future. That must be our focus over the course of this campaign.

“The challenge for Labour today is to defend our values, retain our radicalism, and to make that relevant to people’s everyday lives. People desperately need and want us to win.”

According to the latest Labour figures, only Lewis and Emily Thornberry do not have the necessary level of support from MPs, with Thornberry having nine nominations.

Starmer is out in front on 63, followed by Long Bailey with 26, Lisa Nandy with 24 and Jess Phillips on 22.