The new Archbishop of Canterbury warned against "pinning hopes on individuals" to solve all of society's problems in his first Easter Sunday sermon.

Justin Welby said a "hero leader culture" in which all trust was placed in one person only led to false hope.

Failing to recognise human failure in any organisation was "naive", he told worshippers at Canterbury Cathedral.

"Put not your trust in new leaders, better systems, new organisations or regulatory reorganisation," Welby said.

"They may well be good and necessary, but will to some degree fail.

"Human sin means pinning hopes on individuals is always a mistake, and assuming that any organisation is able to have such good systems that human failure will be eliminated is naïve."

He said: "Human fallibility recognised, God's sovereignty trusted -- these are also the only stable foundation for human beings in society."

The leader of the world's 80 million Anglicans pointed to newspaper reports on Friday that only 40 percent of churchgoers are convinced that he can resolve the problems of the Church of England.

"I do hope that means the other 60 percent thought the idea was so barking mad that they did not answer the question," Welby said.

In a radio interview before the sermon, the archbishop said the Church of England must show it can manage disagreement "gracefully" over issues such as women bishops and gay marriage.

Welby said the Church faced the "challenge" of showing society that its members can hold different views but still remain "gracefully and deeply committed to each other".

Only once it could show it was capable of reconciling different viewpoints could it be a "sign to the world" of peace and reconciliation, he told Premier Christian Radio.

Welby, a 57-year-old former oil executive who was only ordained in 1989, was enthroned on March 21.

One of his predecessors as Archbishop of Canterbury, George Carey, on Saturday accused Prime Minister David Cameron of making Christians feel marginalised because he had backed the legalisation of gay marriage and other policies.

Carey spoke out following comments Cameron made at a pre-Easter reception for faith leaders at which he urged them to oppose "aggressive secularisation".

"It was a bit rich to hear that the prime minister has told religious leaders that they should 'stand up and oppose aggressive secularisation' when it seems that his government is aiding and abetting this aggression every step of the way," Carey said.

But Cameron used his Easter message to hail the "incredible role" played by Christian churches and organisations in Britain and across the world.

"As long as I am prime minister, they will have the support of this government," he said.