William Gardiner (1808-1852)
Following some Googling: There are several Gardiner's in the database variously William G, Mr William G, W G junior etc...
William Gardiner from Dundee either 1808 or 09 to 1852, who was also known as "junior" having a botanist father of the same name, seems to fit most of them.. Two links to biographies are: From the Lamb Collection at Dundee library http://www.dundeecity.gov.uk/lamb/gardiner.htm and a biography from Mark Lawley at http://rbg-web2.rbge.org.uk/bbs/learning/bryohistory/Bygone%20Bryologists/WILLIAM%20GARDINER.pdf give details of his life, collecting and associates.
Around the same time another botanist, George Gardner (NB no "i"), 1810-49 was also active internationally and in Scotland whose biography is at: http://www.electricscotland.com/history/other/gardner_george.htm Seems both George and William were both in contact with Hooker throughout lives..