The Scottish actor appears in a supporting role in Jonathan Glazer's upcoming science fiction film, playing a man who encounters Johansson's humanoid alien Laura.
"At first I was really nervous to meet her but she's nice and laid back, she made me feel relaxed and confident," Brannigan told Digital Spy. "She gave me some nice comments about my timing which boosted my confidence."
He added: "She uses her looks to try and seduce you. I try and seduce her to start with."
Asked if he improvised any of his own chat up lines on Johansson, Brannigan said: "I can't actually remember because I was a wee bit p*ssed at the time! We were having a drink together. We had the script and then you just fling in the odd line yourself. Y'know, 'You have beautiful eyes'."
The Angels' Share opens in UK cinemas today (June 1). Under the Skin completed filming in London and Scotland earlier this year and will be released by StudioCanal.
> Ken Loach interview: "A film has got to demand to be made"
Photo gallery - Scarlett Johansson films Under the Skin:
Copyright: Rex Features Daniel Gilfeather