An increasing number of Massachusetts Health Connector customers are shopping around and switching health plans, state health authorities said Thursday.

Of the 55,000 consumers facing premium increases higher than 15 percent, nearly 13,000 have chosen an alternative plan, usually shifting to lower-cost plans such as Tufts Health Direct, the Connector’s most popular plan. Calls and visits to customer service have increased, along with website usage, another sign of more shopping around.

Officials with the Connector, which serves people who buy health insurance on their own, are expecting a flurry of activity this month as people start receiving their January bills.

Compared with other states’ health insurance exchanges, rates on the Massachusetts Connector are among the lowest.

The Connector has 227,000 members currently enrolled for 2017 coverage. Most are holdovers from this year, but more than 16,000 new enrollees are in the process of signing up and more are expected.

Connector officials said they hope customers will act soon — otherwise they may get stuck with bills they can’t afford.

It’s a hazard of a surprise situation facing the Connector.

Most Connector health plans raised 2017 insurance premiums only slightly, and some even lowered rates. But a couple of insurers posted big, unexpected increases. Neighborhood Health Plan, for example, increased premiums by an average of 21 percent for subsidized plans in 2017.

A significant minority of Connector customers — some 55,000 people — are enrolled in plans with prices going up more than 15 percent next year. If they don’t switch, they will be automatically re-enrolled in their current plan.

The Connector has sent e-mails and paper letters, and placed robocalls to members facing big increases, urging them to act.

But Dimitry Petion, a member of the Connector’s governing board, said Thursday some members may not pay attention to their mail, or may move around so much they never get the message.

“We have a significant number of people who may get into a debt situation . . . that they may never be able to pay off,’’ Petion said.

Board member Nancy Turnbull noted that many lower-income Connector members are accustomed to paying nothing for their coverage; reductions in state subsidies in 2017 will mean that some will be charged for the first time. “We really changed their reality a lot,’’ she said.

Louis Gutierrez, the Connector’s executive director, said the agency is doing everything possible to reach members facing premium increases, but in the end customers have to make their own choices.

The deadline to pay for January coverage is Dec. 23. Those who miss the deadline can still switch plans — if they act before the end of January. But they will be responsible for paying the January premium for their original health plan.

Speaking at the Connector board’s monthly meeting Thursday, Gutierrez said it appears the message is getting out. “We’re seeing the kind of activity we want to see,’’ he said.

Felice J. Freyer can be reached at felice.freyer@globe.com. Follow her on Twitter @felicejfreyer.