Homeless people living on the streets of New York City are being left out in the cold — and out of control — due to Mayor Bill de Blasio’s decision to cut $1 billion from the NYPD’s budget, The New York Post has learned.

Nearly 2,500 complaints to 311 about vagrants desperately needing help or causing problems have been closed without any action by cops who no longer have jurisdiction, according to official data obtained by The Post.

Before de Blasio stripped the NYPD of $4.5 million a year for its Homeless Outreach Unit, the monthly number of those cases was just 79 in June, the statistics show.

But following the budgetary move — prompted by protesters who camped out in Lower Manhattan to demand that Hizzoner “defund the police” — it immediately skyrocketed more than 550 percent, to 437, in July.

The monthly figures have remained in triple digits ever since, reaching a high of 681 in August and totaling 2,486 in just the past five months.

Sources blamed City Hall for failing to have the Department of Homeless Services take over the complaints, as de Blasio promised when he detailed his cuts to the NYPD’s budget.

At the time, de Blasio claimed that civilian workers “can handle this work and that transition will happen in the course of this fiscal year.”

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But with temperatures dropping as winter settles in, no one has replaced the 86 cops formerly assigned to the since-disbanded Homeless Outreach Unit, sources said.

“City Hall took the responsibility away from the [Police] Department but the city never developed or implemented the plan by DHS to handle additional homelessness calls,” an official familiar with the situation said.

The block hardest hit by the official inaction is Manhattan’s West 72nd Street between Broadway and West End Avenue, where the NYPD closed out 57 complaints without responding, according to the 311 data.

Residents said they’d noticed the change that’s taken place since June, with one complaining about an unhinged homeless man who’s been plaguing the area lately.

“He is quite vociferous. He yells and he screams,” said Nancy Lowe, 90, who’s lived in the neighborhood since 1968.

“It was getting better but now it’s getting worse. The police do not come around anymore.”

Another woman who’s lived in the area for 68 years said she’d seen “about an 80 to 90 percent spike” in the number of homeless people.

“Nobody is doing anything. It’s just a deterioration of the neighborhood,” said the woman, who gave her name as Grace M.

“It seems like what I saw in the ‘80s.”