Cheshire Henry Private 1201 8th Hussars (King's Royal Irish) Severe Wound Action at Balaklava 25 October 1854
Assuming he was discharged to pension as a result of his wound, his "service" documents should be available at the National Archive in documents series WO97. Specifically WO97/1728 - details obtained from the catalogue [PROCAT] see http://www.nationalarchives.gov.uk/http://www.nationalarchives.gov.uk/ ,from home page see Home > Getting Started > and follow the links for Army and relevant dates.
WO97 = Royal Hospital Chelsea: Soldiers Service Documents; subseries Cavalry 1728 = names Chas - Col 1873-1882
Records can be ordered online from the National Archives but you will need to specify you require pages for records pertaining to Henry Cheshire etc. Alternatively you may wish to consider using a researcher. You can see a list of researchers on the National Archive's web site. From red menu bar select Getting Started > Independent Researchers > choose a research area; select Army - Genealogy etc , click find researchers select from list [it's worth scroll down the list and checking those with web sites eg J Collins] Final choice must be yours though.
You will find some details about the regiment and links on the regiments page of The Land Forces ofThe Land Forces of Britain, the Empire and Commonwealth web site [regiments.org] at http://regiments.org/regiments/uk/cav/D08h.htmhttp://regiments.org/regiments/uk/cav/D08h.htm