Shameless
aka Mad Dogs and Englishmen
1995
Role: Tony Vernon-Smith

Screen captures
Video of JB's scenes

Jeremy has about 6 total minutes in this very rough movie in which he plays a lecherous, drug-dealing aristocrat. 

He regretted the film, saying in an interview: "I was mad to do it, but I wanted to show the world that I was still alive and I could do other things apart from Sherlock Holmes. I hope they don't release it.

They did release it, and at least reviewers note that Jeremy is the movie's lone highlight. For instance...

A June 4, 1995, review in The Independent (London):

The sole moment of interest came from Jeremy Brett as the aristo swine in charge of the drug orgies. When the police finally burst in, he waves a languid arm and says, "Arrest them all, they are beginning to bore me."

An online reviewer:

He stole the movie even if he was only barely in it. I only wished the director has used Brett to his fullest talents instead of as an aside eccentric. ... Brett's booming voice, subtle expressions and dynamic presence wakes you up for just long enough to pay attention to his character. Once he disappears from the screen, you realize all too soon that the rest of the film is worthless.

DVD available: Amazon U.S. // Amazon U.K.

IMDb page