Allen, 52, is the fourth LAPD officer to be killed in an accident this year. A fifth officer died last week from a heart condition.
The vehicles collided on the 1000 block of Loma Vista Drive at 1:53 p.m., near the scene where a trash-hauling truck lost control and overturned in March, landing on an LAPD patrol car.
The cement truck driver was hospitalized in unknown condition. Beverly Hills police originally reported two people were killed.
LAPD Chief Charlie Beck said Allen was a 25-year veteran of the force, and personally knew him.
"I've known him for several decades. He was a fine family man and he will be sorely missed," Beck said.
Allen worked in the department's Southwest Division and had been previously assigned to the 77th Street, Wilshire and Rampart areas. He leaves behind a fiancee, his mother, two children, two grandchildren, and a sister.
Loma Vista Drive was shut down from Doheny Road to Drury Lane for the remainder of the evening Friday. The incident was under investigation.
Beverly Hills suspended all heavy-haul deliveries to and pick up from construction sites in the area known as Trousdale for 30 days or until measures are in place to ensure that the deliveries can be made safely, the city announced in a statement Friday night.
Signage will be posted in the area to prohibit heavy delivery to the area, the statement said.
Officer Nicholas Lee, a 16-year veteran, was killed, and his rookie partner was critically injured when a trash-hauling truck traveling downhill on Loma Vista Drive turned over as the cruiser was traveling uphill, landing on the police car Friday, March 7.
A cement truck was traveling on the same street when it struck six parked cars and overturned last Friday.
L.A. Mayor Eric Garcetti released a statement Friday afternoon: "The city is still reeling from the recent death of three on-duty LAPD officers, and my heart aches at the death today of yet another of our officers. Amy's and my thoughts are with his family and everyone in the Los Angeles Police Department. This is a difficult time for our men and women in blue, and the whole city joins them in mourning the loss of these heroes."
The department is still mourning the recents deaths of Officer Chris Cortijo and Officer Roberto C. Sanchez. Cortijo's motorcycle was rear-ended by a driver alleged to have been under the influence of cocaine in Sun Valley on April 5.
Sanchez was struck and killed after his patrol car was broadsided while chasing a speeding car in Harbor City on May 3. The driver has since been charged with murder.
On Saturday night, LAPD officers and their supporters gathered for the True Blue Gala event at the 20th Century Fox Studios. The annual fundraiser is usually a festive event. But this year, officers wore black bands over their badges to mourn Allen's death.
