City Council Speaker Christine Quinn took a sharp left turn in her State of the City speech yesterday, reminding voters she is a liberal Democrat and distancing herself from Mayor Bloomberg as she gears up for a competitive 2013 mayoral primary.

The Manhattan Democrat — who veered to the political center in recent years by aligning herself with Bloomberg and sympathizing with businesses and the city’s political centrists — criticized Hizzoner’s stewardship of the public-school system.

Quinn called for the expansion of a system that would increase collaboration among all schools in the Department of Education, and announced support for mandatory kindergarten and a new “honors college” campus at the City University.

She also blasted the New York City Public Housing Authority as being on the verge of “another form of substandard housing” and promised a $10 million council allocation to repair the agency’s homes.

“It was a hard left — it hurt my neck,” joked Councilman Peter Vallone (D-Queens).