Professor Russel Griggs has been called on to investigate why the new scheme seems to be failing to take off.
The Treasury has yet to release the officials figures from the scheme and has not set targets.
However, The Times has reported that “there is disappointment among officials at the lack of activity”.
The scheme, which began in November 2016, was designed to widen SME access to finance and encourage them to look beyond traditional lenders.
Upon refusal of a loan, businesses must be referred to one of three finance platforms – Funding Options, Funding Xchange and Bizfitech - that will suggest routes to alternative finance.
The banks involved in the scheme include RBS, Lloyds, HSBC, Barclays, Santander, Clydesdale and Yorkshire Bank, Bank of Ireland, Danske Bank and First Trust Bank.
Griggs’ role is to assess, and suggest improvements to, the referral processes of each of the designated banks.
“We welcome the role Russel Griggs is playing in ensuring that the scheme is as effective as possible for small businesses,” a spokesperson from the Treasury said.
He is currently a board member and chair of the audit committee of Lenlyn Group, as well as board member of Audit Scotland, and member of the audit board to the auditor general for the States of Jersey.
"We welcome professor Griggs' support in facilitating best practice across the industry in respect of bank referrals to finance platforms," a spokesperson from the British Banking Association said.
"The industry supports the aims of the referral process in giving businesses, if they wish, the opportunity to be referred to the widest possible variety of finance options through the designated platforms."
The banking industry has been working with professor Griggs for more than five years in his role as independent reviewer of the Lending Appeals Process.
Last month, the owner of Clydesdale and Yorkshire banks, CYGB, pledged a minimum of £6bn of lending to be made available for SMEs between 2017 and 2019.