The heads of the Anglican and Catholic churches in the UK received a standing ovation at the Royal Albert Hall after praying for Christian unity and talking openly about the challenges of achieving it.

The Archbishop of Canterbury Justin Welby and the Archbishop of Westminster Cardinal Vincent Nichols were interviewed on stage at the HTB Leadership Conference by Nicky Gumbel, in what Gumbel called a "historic" moment.

The two leaders discussed their friendship, and spoke about initiatives around which they've united, such as working against human trafficking. "What joins us together is that sense that is is the Lord Jesus Christ who reaches out to us and calls us together," Welby said. "The call of the Church [is] to repent of our divisions and seek unity in Christ so that the world may know Jesus."

Nichols and Welby are both credited with establishing warmer relations between the Anglican and Catholic Churches; it is the disunity of the Church that destroys peace, Welby said. "We destroy the peace of the Church and the Church's capacity to be a peacemaker, to bring the peace of Christ to this world, when we are not peaceful with each other – when we fight, destroy and tear each other, as Paul said to the Galatians."

Nichols explained that he and Welby have "an implicit trust in each other", which has not always been the case with Anglican and Catholic leaders. "It is not something that is heavy, that we work at because it's an uphill struggle, but it's much more like a breeze coming from behind us that catches our sails and helps us to go forward," he said.

They both spoke with great respect about Pope Francis, and of his commitment to unity. Francis emanates a "profound sense of global authority, a profound sense of global wisdom... a deep commitment to human relations and above all relations both with the core and those on the edge," Welby said.

"When we've met we've talked principally about prayer, the Lord Jesus Christ and the poor. I've come away from each meeting with a renewed determination and inspiration...[to be] drawn back to the face of Christ."

Nichols thanked the Pope for helping people to see the Christian gospel in a new way, and the Catholic Church "through fresh eyes". He praised Francis' humility and rootedness, sharing that the Pontiff had told him that he had never once lose his sense of deep peace since taking on the role.

"We need people to see our unity," Welby added. "If invisible symbols were effective, Jesus need never have been born as a human being. But visible symbols reach out and break into the hearts of human beings [and] demonstrate the reality of the love of God in Jesus Christ.

"When we are visibly united, it speaks more powerfully to the world...than we can ever begin to imagine, and we cripple our witness when we are not united," he added. "We release a power of witness in the world of who Jesus is, of hope, [and of] life."

There was strong sense of the personal importance of unity to the three leaders on stage. They also appeared to be in agreement about how to bring it about – a combination of human endeavour, God's leading and love for one another.

Reconciliation is "not something we negotiate and construct," Nichols said, "but something we receive in two places: on our knees and in the service of the poor."