It could take a decade for Barclays to win back the public's trust, the bank's chief executive has admitted.

Antony Jenkins said the series of scandals that have rocked the banking system, including the mis-selling of payment protection insurance and Libor fixing, had damaged the bank's reputation over the long term.

"Trust is a very easy thing to lose, and a very hard thing to win back. In my view it will takes several years – probably five to 10 – to rebuild trust in Barclays," he said.

"I can only be responsible for Barclays but I'm hoping in what we do at Barclays we can also rebuild trust in banking."

He made the comments to students at Brooke House Sixth Form College in Clapton, east London, featured on BBC Radio 4's Today programme, which Jenkins guest edited on Tuesday.

During the conversation the Barclays boss said he was setting his bank a target of being more trusted than not by 2018, the reverse of which is true now according to the bank's own research.

Jenkins, who was appointed chief executive in August 2012 after his predecessor Bob Diamond was forced to step down over the bank's role in the Libor scandal, expressed frustration that too much emphasis is placed on short-term factors such as share prices.

Jenkins invited Justin Welby, the archbishop of Canterbury and one of the City's toughest critics, to participate in the Today programme.

Welby spoke of the need for "justice and hope" in the future of banking in his Thought for the Day. The archbishop, who, as a member of the parliamentary commission on banking standards, clashed with Jenkins earlier in the year over the culture at Barclays, appeared to build bridges with the bank boss.

"People like Antony [Jenkins] are dealing with the impact of 30 years, in which there was strong pressure to go in one direction, which was about maximising shareholder return and a progressive loss of vision as to what banks were for in society," he said.

"The challenge for leadership is to change that culture, that says we are not here just for ourselves, we are here for the whole of society, and that is a massive, massive challenge and will take a very long time to turn around. Barclays are working very hard at it and the major banks are working very hard at it."

Welby did however criticise senior banking executives in some parts of the industry who he claimed refuse to acknowledge any responsibility for the financial crisis which took hold in 2008.

"I don't want to name names but I came across some people recently – senior members of the City from foreign organisations – who were very clearly still absolutely in denial about what happened in 2008."