Which Earl Fitzwilliam is this?

I can't see a year date shown on the cover - some of the peerage lines not easy to follow, but looks like 6th Early Fitzwilliam died 1902, which would probably give workable time line for this cover. The 6th Earl had two daughters, Lady Alice Wentworth F. born 1849, and Lady Charlotte Wentworth F. born 1858 - so that also fits reasonably well.
Ref. Kelly's Handbook to the Titled, Landed and Official Classes 1920.

I'll throw my hat in the ring and guess the 5th.  My best guess for the date of the red ink rounded-off-sort-of-a-shield-shape postmark is Mar 31, 1854 (day & month are clear enough, so is the "18", the 3rd digit is entirely missing but can only be a "4" or a "5", and the 4th digit seems more like a "4" than anything else).  The dark ink sideways script on the front of the envelope seems clear enough to be "April 1", the "185" is reasonable enough, and the "4" is again sort of a best guess.  As mentioned on the pencil notation on the back of your cover, the "1 A^N 1" stands for a time of 1:00 PM.

 

The pre-stamped envelope looks to me like the 1850-51 design according to my Michel Ganzsachen catalog, the only source I have for British postal stationery listings.

The following snip is from the October 2002 issue of Notebook, the journal of the London Postal History Group.  The lumpy red shield with the code letter at the bottom of the frame was in use until some time in 1858, according to them.  5th Earl Fitzwilliam died in October 1857, so there is a possibility that it could still be the 6th who is the addressee if the guesses on the dates are wrong.  (It should be noted that your example, and at least one other I've seen, has the date line on the top and the year on the bottom, opposite to what this listing specifies, so that leaves a possibility that there is something wrong with my research somewhere.)



Ryan