Jane
Royal Greenjackets Museum.
http://www.rgjmuseum.co.uk/research.asp
According to the website they do not hold individual records.
I have written them (not e-mailed) in the past and received a response. I have not contacted them recently.
For individual records they suggest consulting the Army Museums Ogilby Trust website.
http://www.armymuseums.org.uk/ancestor.htm
The National Archives in the UK also holds service papers.
http://www.nationalarchives.gov.uk/
You can research personally, have the Archives research for you (for a fee) or hire a Research Agent to research for you.
Also Library and Archives Canada holds a number of British Army records. They had my GGGrandfather's British Army service papers, for example. You could try there.
http://www.collectionscanada.gc.ca/
Good hunting.
Ron