There are 12 Royal Letter locations in the game. Finding all of them unlocks the A Life in Letters achievement.
There is no map to buy for this kind of collectibles, luckily all 12 Letters are located in the Westminster Discrict of London. All Royal Letters are saved automatically when picking them up.
You can check under Database - Encyclopedia - Collectibles - Royal Correspondence which letter you have and which not.
Timeline:
*** Spoiler - click to reveal ***00:06 - Letter #1 (June 26, 1867)
00:36 - Letter #2 (October 14, 1867)
01:05 - Letter #3 (December 19, 1867)
01:34 - Letter #4 (December 16, 1867)
02:04 - Letter #5 (May 22, 1867)
02:33 - Letter #6 (April 27, 1865)
03:05 - Letter #7, #8 (February 6, October 16, 1866)
04:03 - Letter #9 (April 29, 1865)
04:41 - Letter #10 (January 22, 1866)
05:13 - Letter #11 (June 13, 1865)
05:49 - Letter #12 (May 21, 1865)