I can only find two Vaughan Williams pieces... Fantasia on a Theme From Thomas Tallis and Fantasia on Greensleeves.
Neither seem to fit. I ran the music clip to a few music historians, so maybe they'll find out.
Faceman: terrific job. The colors looked really dull on the field. Judging from other adjoining shots, they were the wrong color since the grass around Tack's cell is bright green, along with where the royals sat.
Also... it might be a good idea to crop the left side of the image a little bit. I found that you can occasionally see the edges of cels. The shot with the eunuchs holding swords to Tack's throat shows that the one on the far left doesn't fill the edge, causing you to see a little ribbon of the background. Also, some moments have visible splice lines - they're not supposed to be visible.