According to the New York Post, some of the city’s best-known eateries are lucky the Health Department is starting to hand out letter grades next week — instead of last month — because thousands would have ended up with a bottom-rung "C" plastered in their front windows.

Officials estimate that about 6,000 of the city’s 24,000 eateries had enough violation points in June to have earned the lowest mark on a three-letter rating scale devised by the city.

The "C" restaurants would have ranged from the Lion, a sizzling new spot in Greenwich Village, to the venerable Gallagher’s steakhouse in Midtown, to the century-old Katz’s deli emporium on the Lower East Side.

Even Radio City Music Hall’s snack bar made the "C" list.

The Health Department plans to award "A" grades to restaurants that accumulate no more than 13 violation points; "B" to those with 14 to 27 points; and "C" for 28 or more points.

Restaurant owners and managers contacted by The Post who would have faced a "C" last month were surprisingly supportive of the grading system.

"It’s for the sake of public health — I’m perfectly OK with that," said Jake Dell, son of the owner of Katz’s deli, which accumulated 47 points on its record for such infractions as evidence of roaches and mice, as well as bad plumbing.

Like every restaurateur contacted, he said the conditions cited by inspectors have since been corrected. A reinspection July 6 brought Katz’s score down to 23 — in the "B" range.

Over 10 years after the Dirty Dining series of articles appeared in the Toronto Star, which led to the creation of the red-yellow-green restaurant inspection disclosure system, and the arguments haven’t changed: people want the information, good restaurants promote their good food safety scores, and the various lobbies think the system is silly.

After watching for 10 years, I figure no politician is going to restrict this kind of information to the public; so figure out the best way to make such information available.

As New York City prepares to adopt a letter-grading disclosure system, similar to that in Los Angeles, the N.Y. Times reports that at a public hearing Tuesday, the health-department announced it had received 280 written public-hearing comments — 273 for, 6 against and one ambiguous. But none of the 80 who attended the hearing came to the plan’s defense.

Vincent J. Mazzone, owner of the Chicken Masters restaurant in Brooklyn’s Sheepshead Bay, told the hearing,

“The premise of the letter-grading is sophomoric, and punitive and demeaning to restaurateurs, as if they are schoolchildren who must be graded.”

Marc Murphy, chef and owner of Landmarc Restaurant in TriBeCa, said that average diners “will see a C grade and no one will come in — they might as well close shop. Everyone in our business is not against health inspections, but we don’t want bad letter grades from trivial infractions.”

In March the board voted 6 to 2, with one abstention, to rate cleanliness in the city’s more than 24,000 restaurants using publicly posted letter grades, compelling operators to post inspectors’ ratings that were previously available only at the department or online.

Under the program the city will supply the placards to restaurants rated with a blue A for the highest grade (from 0 to 13 points under the old system), a green B for a less sanitary but still passing rating (13 to 27 points), and a yellow C for a failing grade (28 points or more). The signs are to be dated, and prominently posted in windows or restaurant vestibules.

Thomas Slattery of the United Restaurant and Tavern Owners of New York told the commissioners

“In L.A., it’s basically a joke — everyone gets an A.”

Guess he’s never heard of C is for Chinese in L.A., but people show up anyway.