Darren Criss, previously best known for his role as clean-cut Blaine Anderson in Glee, said he told executive producer Ryan Murphy: “I don’t want to flatter myself but if you can find someone else my age who looks like him and is half-Filipino like he was, then sign them up.”

Cunanan preyed on rich, gay men and was obsessed with Gianni Versace. He murdered at least five people culminating with the shooting of the designer himself in 1997.

Criss’s portrayal has won plaudits from audiences and critics alike and on a whistle-stop visit to London to promote the show and perform a concert, Criss says how little was known about Cunanan’s killing spree before the show was aired.

“Unless you happened to be living in Miami, certain gay communities in San Diego or worked in real estate in Chicago, these were localised things you just wouldn’t have known about,” he explains.

The Assassination Of Gianni Versace: American Crime Story reaches its finale on Wednesday and hints at the homophobia that may have been behind the FBI’s reluctance to investigate the killings.

In one scene some leaflets about Cunanan’s activities are shown still stored in the car boot of a police car.

This, combined with the reluctance of many gay men to speak up – some had survived the Aids scare – allowed the outwardly charming and apparently wealthy Cunanan to stay at large.

“He was not like Jeffrey Dahmer or Charles Manson, whose behavioural patterns all pointed to their eventual homicidal behaviour,” explains Criss, 31, who says of those who knew Cunanan during his teenage years very few had anything negative to say about him.

“One woman, in particular, said to me, ‘I just remember Andrew being so much fun. He was so good to me, he was so sweet. He was just someone you could count on’.”

What curdled Californian-born Cunanan’s character above all, the actor suggests, was that his beloved father, a broker, turned out to be an embezzler who fled to Manilla having sold the family’s house out from under them. The series also hints he sexually abused his son.

“His father was his hero but when your hero does that you can do one of two things. You can either change your way of thinking and shift your adolescence or you can just cover up the stench with more perfume.”

Cunanan chose the latter. He lied to friends and employers that his father was a rich man who owned pineapple plantations in Manilla. Eventually he began lying about himself, enriching his own career and experiences to ensnare and live off the money of wealthy men.

“One day he’d be a rich Israeli, next he was a French diplomat or the designer of the sets for Titanic. It was all delusional.”

The TV series was structured to play the events in reverse order, from the Versace killing to both the victim and killer’s early lives. “It’s almost willing the audience, who already know what he did, to try and find some redemptive qualities in him,” says Criss. Whether they do or not, he says, is up to them.

“Obviously what he did was deplorable and unforgiveable, and nothing positive about him exonerates that. But [his story] questions the complexity of the human experience. We are all as capable of murder just as we are all as capable of having a wonderful night out with friends.”

How I won the role of Versace’s killer Andrew Cunanan