The Labour leadership contender Lisa Nandy has backed removing references to the British empire in the honours system, saying it should recognise “British excellence” instead.

At a hustings in Bristol on Saturday, Nandy said the honours system should be a tool to bring people together, rather than shut them out.

Nandy, who is still seen as an outsider in the race despite strong performances in early hustings, said: “It was [poet] Benjamin Zephaniah who balked at the prospect of accepting an OBE – the Order of the British Empire. Why not a choice to provide the Order of British Excellence? Why does the honours system, which should recognise the contribution of our people, shut people out, rather than bring people in?

“That is the country I want to build, and the Labour party I will lead. That never accepts the world as it is but builds the world as it should be. As Benjamin Zephaniah asked: ‘What happened to the verse of fire?’ We can be far more ambitious.”

The move by Nandy is the latest pledge by leadership candidates designed to appeal to Labour’s leftwing membership, which expanded hugely under Jeremy Corbyn’s leadership. Nandy’s pledge came as leadership contenders clashed over the selection of Labour MPs – an issue that has regularly caused divisions.

Rebecca Long-Bailey, the candidate closest to Corbyn, reiterated her pledge to bring in open selections if she was elected leader, a move that would in effect allow local Labour activists to deselect their MP. She said being an MP was “not a job for life”. However, she was challenged by Nandy, who warned against focusing on the party’s internal power struggles. “The MPs I want to get rid of are Tories, not Labour,” Nandy said.

The candidates also clashed over Brexit during the first hustings event since Britain’s departure from the EU. Long-Bailey and Nandy called on the party to accept Brexit and move on. However, the pro-remain shadow foreign secretary, Emily Thornberry, who still lacks the necessary grassroots support to appear on the leadership ballot paper, said the bumpy negotiations ahead meant Labour needed a leader who had been “on the right side of the argument all along”.

Long-Bailey said the party’s next election campaign must not be based on “we told you so” over the dangers of Brexit. The shadow Brexit secretary, Keir Starmer, who helped steer Labour towards backing a second referendum, said the debate around leave or remain was over. However, he accused the government of failing to tackle the issues that led to the Brexit vote.