By Bad Seed
Well, I found that already uploaded on YouTube, but in a poor quality, and not the full scene. Also, it wasn't linked to Jeremy Brett (nor to Bill Shirley, who - unneccessarily, really - dubbed his singing voice). I love this scene since my childhood; and it's a marvellous song by Frederic Loewe (music) and Alan Jay Lerner (lyrics).
Finally, this is some sort of sentimental reminder for me. I was among those who, after the last performance of The Secret of Sherlock Holmes, stood at the Stage Door of the Wyndham's Theatre and sang it to Jeremy Brett, who really was up in tears. May he rest in peace.
"Cameos" in this scene: the great Mona Washbourne and the inimitable Rex Harrison, playing George Bernard Shaw's Holmes substitute Henry Higgins.
Go, buy the DVD! It's a great movie! =)