The Wire star plays Burton opposite Helena Bonham Carter as Taylor in upcoming Tv movie, Burton and Taylor.
The pair threw themselves into playing the famously fiery couple, and West was blown away with how exciting their daily lives were after flicking through an article by Burton on the set of the biopic.
He tells Britain's The Sun, "On set there was a 1971 edition of Vogue, just as set-dressing, and inside there was an article by Richard Burton - it was called One Day In My Life.
"He and Liz were in Puerto Vallarta, in Mexico, and the circus had come to town. They went to the circus and the ringmaster spotted Liz and called her out.
"He attached her to this big board and spun her round and started throwing knives at her. Burton went crazy. He was trying to stop them. But she said: 'Oh, Richard, leave him. You're making him nervous.' Then they tried to get Burton to do it and he said: 'No f**king way!'
"The article ended with them both back home, getting into bed and Liz turning out the light and going: 'Well, another interesting day.' They had this incredible double act and were brilliant together as actors as well. That's what was so magnetic about them."