Business owners, investors and family office principals are putting their personal reputations at risk by not taking steps to narrow pay gaps in their companies, a new national survey has found.

The new survey found that more than 63 percent of the UK public would think worse of the wealthy owner of a company if they found out that one of the businesses in their portfolio had a poor gender pay gap.

Similarly, 58 percent of people would think worse of a company owner if one of their businesses was perceived to have unfairly large pay differentials between entry-level employees and executives.

While studies have...