In an open letter to chancellor George Osborne, Mr Green - writing in his capacity as chairman of the British Bankers' Association (BBA) - said that the taskforce will include members of the Bank of England and the Treasury.
"We, like you, believe there is a real need to make sure that viable businesses are able to obtain the finance they need to support the recovery of the UK economy," he stated.
The findings of the body will be presented to the chancellor in October.
Earlier this month, BBA chief executive Angela Knight said that the return to profitability at many banks is helping the UK to move out of recession.
She added that financial institutions still face lending difficulties as a result of the expectations on them to increase the amount of capital they hold.
By Tony Aynsley