Hi again Jigsaw
I can see why you think your grandfather may have been in the Yorkshire Regiment at some point, but this may turn out to be incorrect.
In the 1901 Census there is an Alexander Wrist, listed as a private in the Yorkshire Regt living in the Sheffield Barracks in Nether Hallam. The trouble is, he is only 18 years old and born in Fulham. [RG 13/4345 folio 167 page 13] Confusingly enough, his full name was Alexander Ernest Wrist! [Birth registered 1883 in Fulham]
Clearly this person was not your grandfather (or even his son) as the age is completely wrong. Additionally, your own family were living elsewhere at the time - Fulham as it happens!
Dave
PS.
Just a note of some of the Census references in case I lose them:
1861 Banstead - RG 9/416 folio 8 page 14 - Alexander with parents James and Mary.
1871 Streatham - RG 10/718 folios 44-45 pages 8-9 - ditto
1881 Wandsworth - RG 11/659 folio 96 page 16 - Father James with second wife. No Alexander.
Can't find Alexander in 1881.
Can't find him 1891 either - Arranroots do you have the ref?
1901 Fulham - RG 13/68 folio 75 page 17 - Alexander with wife Eliza