Jeremy Corbyn held out the "hand of friendship" to his detractors in Labour's parliamentary party during his leadership campaign launch speech this morning (21 July), while warning that all Labour MPs could face reselection.

The left-winger insisted that the party was "stronger" under his leadership, citing Labour's by-election victories since his election and the May election results, which saw Sadiq Khan become Mayor of London and Marvin Rees be elected as Mayor of Bristol.

But Labour MPs overwhelmingly backed a motion of 'no confidence' against Corbyn over his EU referendum performance, a vote which saw Labour heartlands across England and Wales back a Brexit.

The leader has also faced mass resignations from his shadow cabinet, including Pontypridd MP Owen Smith who is now challenging him for the leadership.

"I say to Labour MPs quite simply this: I've been in parliament a very long time, I've seen lots of leaders, I've seen them come and I've seen them go, there is a huge amount of talent on the Labour benches," Corbyn said.

"We are part of, but not the entirety of, the Labour Party and the labour movement, and I hope those who may not agree with me politically, may not even like me personally – I find that hard to believe – I hold out the hand of friendship."

Corbyn also said Smith would be "very welcome" if he re-joined his shadow cabinet after the leadership election, which will finish on 24 September. But the leader warned all 230 Labour MPs could face reselection after the 2018 boundary review, which could change the shape and size of constituencies across the country.

"There would be a full selection process in every constituency but the sitting MP would have an opportunity to put their name forward," he said. "So there will be a full and open selection process for every constituency Labour Party through the whole of the UK."

The comments come after major trade union Unite, a large Labour donor and backer of Corbyn, recently voted to back the reselection mechanism for Labour MPs. The Labour leader also promised to tackle the so called "five ills" of British society, including inequality, neglect, insecurity, prejudice and discrimination.

"In my campaign I want to confront all five of those ills head on setting out, not only how Labour will campaign against these injustices in opposition, but also spelling out some of the measures the next Labour government will take to overcome them and move decisively towards a society in which opportunity and prosperity is truly shared in which no individual is held back and no community left behind," he declared.

Corbyn also said he would force employers with more than 21 staff to publish equality pay audits to detail remuneration levels, grades and hours of every job alongside data on recognised equality characteristics "because it is not only women who face workplace discrimination, but disabled workers, the youngest and oldest workers, black and ethnic minority workers."