The 40-year-old shot a sex scene with actor Javier Bardem for the film on the bonnet of a yellow Ferrari at Stoke Park golf course, Buckinghamshire.
And an ex-SAS squad and dog unit were apparently carefully positioned around the course and in the trees to ensure passers-by or fans could not see what was going on, reported Sun Online.
"It was like a military operation. Producers had thought of everything to stop any intruders possibly getting a glimpse," a source said.