London —

Democratic leaders must answer to voters, lawmakers and other world leaders. But Britain’s likely next prime minister will need to win over another powerful audience: the bond market.

Andy Burnham, the charismatic former mayor of Greater Manchester, once rebuffed the idea that government decisions should be swayed by investors in its ballooning pile of debt. In September, he told the UK’s New Statesman magazine that he wanted Britain to go “beyond this thing of being in hock to the bond markets.”

His comments reflect a growing perception that bond investors, not elected officials, have become the de facto authority on how Downing Street decides to tax and spend. When investors view policies as too expensive, they effectively punish the government by dumping bonds because holding the debt is seen as too risky. And when a bond is dumped, its yield — or the interest the government must pay new investors in those same bonds — rises. That increases borrowing costs across the wider economy, including people’s mortgage rates.

Burnham, now with the inconvenient realities of leadership in sight, has since softened his stance, telling ITV News last month that he supported the ruling Labour government’s fiscal rules and wanted to reduce the public debt.