Ogilvy has had an extensive career in the theatre playing leading roles in many London West End productions, including Design for Living, Happy Family, Three Sisters, Rookery Nook by Ben Travers, Run for Your Wife, The Millionairess by Shaw, The Waltz of the Toreadors, and others. He has also worked widely in the American theatre. Among his films, Ogilvy had a major part in the 1970 epic film Waterloo.