Barclays chief executive Bob Diamond is facing calls to resign after the bank was fined £290m for trying to manipulate a key bank interest rate which influences the cost of loans and mortgages.
Former chief executive of Barclays Martin Taylor told the programme that it is "hard to believe a policy that seems so systematic wasn't known to people at or very near the top".
"If you are going for a policy of systematic dishonesty you have a lot of rebuilding to do," he said.
He said the chief executive of a bank does not always know what is going on "but they set the tone".
"If Bob Diamond can help clean up the stables then he should stay," he told John Humphrys, but said that only the board of Barclays can decide.
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