San Franciscans appear to be warming to the idea of building denser housing around transit hubs, an issue that has proved to be divisive in the city and across the Bay Area.

An annual state-of-the-city poll commissioned by the San Francisco Chamber of Commerce revealed that 74 percent of the survey’s 500 respondents supported a state bill that would, among other things, prevent cities from restricting apartment construction within a half mile of a transit station, like BART or Caltrain.

Though it wasn’t mentioned by name, the poll was asking respondents about SB50, a bill by state Sen. Scott Wiener, D-San Francisco.

The survey results could suggest a shift in the city’s sentiment toward increasing density around transit hubs, a move that proponents have long held is essential for a city and a region tormented by traffic congestion and a punishing housing shortage. Prominent officials at the local and state levels, including Mayor London Breed and Gov. Gavin Newsom, have also struck a strong pro-housing stance, which could be helping to emphasize development.

The survey framed the bill’s purpose as adding housing around transit stops “so people could live closer to where they work.” According to the chamber’s poll, 82 percent of respondents said traffic in the city had worsened, 69 percent said parking is harder to find, and 63 percent said it is harder to find housing for people like themselves.

Critics of the bill, however, blanch at the prospect of surrendering local control to the state and express deep concerns about how new developments could distort neighborhood character. Twenty percent of respondents said they “somewhat” or “strongly” opposed the bill, and 6 percent said they either didn’t know, or preferred not to state their opinion.

The chamber will release the full results of the poll, which acts as a barometer of people’s attitudes on a range of city issues, including homelessness, public transportation, Tuesday morning.

The legislation also raises height limits to 45 feet, about four stories, within a half-mile of the station, and 55 feet within a quarter mile. It also eliminates minimum parking requirements for new developments, which San Francisco’s Board of Supervisors voted to do back in December.

“All the polls I’ve ever seen on this show strong support, but this is strongest,” said state Sen. Scott Wiener, D-San Francisco. “I’m thrilled to see public opinion continue to shift in a pro-housing direction. At some point you reach a breaking point.”

Notably, support for the bill was spread out fairly evenly across the city’s supervisorial districts, according to the poll’s results. The city’s western districts — populated largely by enclaves of single-family homes — have long been the center of opposition to new developments in the city.

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But District Four, which includes the Sunset, had the highest percentage of respondents say they “strongly” or “somewhat” supported the bill — the most of any district.

SB50 represents a lighter version of legislation Wiener introduced last year. That bill, SB827, would have kept cities from rejecting four- to eight-story apartments or condos near transit hubs.

The bill exposed transit-oriented housing as a major fault line in San Francisco politics, and ultimately couldn’t get out of the Senate Transportation Committee, where it was killed by a 5-4 vote.

It drew strong opposition from local leaders, most of whom supported transit-oriented housing, but criticized the bill for not exacting enough concessions from developers and warned that new development would lead to further gentrification and displacement of middle-class and low-income communities.

San Francisco’s Board of Supervisors voted 8-3 to oppose the measure.

“Living where you work is important to maintaining a strong economy for the entire Bay Area,” said Juliana Bunim, senior vice president at the chamber, which supported Wiener’s SB827 and his current bill.

“Everyday we hear from our members how their employees can’t afford to live here and are being forced to leave. It’s time to talk about what real solutions are for housing and not get distracted by a couple of loud voices that can drown out what people actually want across the city.”

Chronicle staff writer Rachel Swan contributed to this report.

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa