Jennie: Lady Randolph Churchill
5 November 1974, miniseries, Thames/ITV
Role: Count Charles Kinsky

Video clip (thanks RJ Doll!)

This was a seven-hour, seven-part miniseries starring Lee Remick as Jennie Jerome, an American who eventually became Lady Randolph Churchill and gave birth to Sir Winston Churchill.

Jennie Churchill had many affairs during her marriage to Randolph Churchill, including Austrian Count Charles Andreas Kinsky, which is JB's role in this miniseries.

IMDb page // Review and synopsis
Synopsis and picture at The Brettish Empire

Wikipedia page about Jennie Churchill  

Wikipedia page about Count Kinsky