Metro Bank is facing a possible shareholder revolt over the re-appointment of its chairman and founder following multi-million pound payments made to a company owned by his wife.
Royal London Asset Management said it was concerned about whether Metro was getting good value by using InterArch.
The firm is owned by Shirley Hill, the wife of Metro chairman, Vernon Hill.
In 2017, Metro paid £4.1m to InterArch for architectural design, branding and marketing.
Challenger bank Metro will hold its annual general meeting in London on Tuesday afternoon where, among a number of resolutions, investors will vote on the re-appointment of Mr Hill.
Shareholder advisory group Glass Lewis has advised investors to vote against Mr Hill's re-election.
Ashley Hamilton Claxton, head of responsible investment at Royal London Asset Management, which holds a 0.44% stake in Metro Bank, said it was concerned about the oversight of the payments to InterArch.
She told the BBC's Today programme: "The concern is whether the company has had sufficient scrutiny as to whether they are getting value for money for those payments."
As well as the payment for 2017, Metro Bank also handed £3.1m to InterArch in the previous year and in its prospectus ahead of its flotation on the London Stock Exchange, it said it paid £2.3m to Mrs Hill's company for marketing and architectural services in 2015.
Under the agreement, InterArch could also claim up to £2,000 per month for services.
Metro Bank said: "Metro Bank has a premium listing on the London Stock Exchange and therefore is fully compliant with the UK Corporate Governance Code by the Financial Reporting Council."
Ms Hamilton Claxton added: "We've also had some concerns in the sense that Mr Hill was also scrutinised in the US for similar payments to his wife's firm when he was director of a company there."
Mr Hill founded Commerce Bank in the US, which he left in 2007 when board members voted to remove him.
The New York Times reported that the bank had paid InterArch around $50m over 10 years to decorate and design Commerce Bank branches.
Metro Bank repeatedly states in its prospectus and subsequent annual reports that its arrangement with InterArch is subject to a review by its audit committee to ensure it is "materially consistent with those that could be obtained from an independent third party".
However, Ms Hamilton Claxton said that Royal London would also vote against the re-appointment of Stuart Bernau, who is the chairman of Metro Bank's audit committee.
She said: "I guess the question is do we think the board is in a position to provide a fair and accountable and objective oversight of the payments and our question is because the firm is linked to the company's chairman, we would want additional scrutiny of those payments."
A spokesperson for Metro Bank said: "InterArch provides architecture, design and branding services to the bank. The audit committee has strong review and benchmarking processes in place conducted by authoritative independent third parties to ensure that the terms are favourable for the bank. This process has been in place since Metro Bank's inception and is disclosed in our Annual Report."
While Ms Hamilton Claxton said it was unlikely Mr Hill would be unseated, she said: "The reason we vote against is to register our concern and then have a dialogue with the company."