WASHINGTON — Most drivers don’t expect to be hit with a rate hike on their auto insurance after a car accident that wasn’t their fault. But a consumer group says it happens, and it’s a problem.

The Washington-based Consumer Federation of America says it found rate increases on annual premiums as high as $400 in some cases.

In a report released Monday, the group analyzed premium quotes in 10 cities, including New York and Chicago, from five of the nation’s largest auto insurers. The researchers found that Progressive aggressively used a not-at-fault penalty, surcharging drivers in eight of the 10 selected cities. Rates in Oklahoma City and Los Angeles did not change. Oklahoma and California prohibit not-at-fault penalties.

The group said GEICO and Farmers raised rates in some states by 10 percent or more. Allstate had occasional penalties. State Farm was the exception, with no increases on premiums for not-at-fault accidents.

“Most people know that if they cause an accident or get a ticket they could face a premium increase, but they don’t expect to be punished if a reckless driver careens into them,” said Bob Hunter, the federation’s director of insurance and the former insurance commissioner of Texas.

The Insurance Information Institute said the underwriting of a new auto insurance policy requires the collection of much more information beyond what the foundation gathered from the auto insurers’ websites.

Loretta Worters, vice president of communications at the industry trade group, says it also is rarely clear-cut as to who the at-fault party is after a collision. But she said one reason rates may rise for the not-at-fault driver is subrogation – when an insurer, after paying a loss, seeks to recover money from the at-fault driver’s insurer.

Among the cities tested, drivers in New York City and Baltimore paid out the most for doing nothing wrong, the consumer group said. In Baltimore, premiums increased more than $250 and in New York City, it was about $400. In Chicago and Kansas City, the average increase was about $100.

The federation found that people with moderate incomes often saw bigger premium increases than upper-income people. That seemed to mirror average premiums even for people with clean driving records and no accidents.