Prior to reforms beginning in 1857 divorce was difficult, if not impossible for most as marriage was governed by church law rather than civil law. It required an annulment, or a private bill to be passed in the House of Commons. Until 1937 divorce laws was one-sided - men could divorce their wives for adultery, but wives could not divorce their husbands unless adultery was proven, and there were additional offences such as incest, sodomy, violence or cruelty.
Records are sealed for 100 years - for a divorce finalised in 1871 they weren't be freely available until 1972. See
http://search.ancestry.co.uk/search/db.aspx?dbid=2465 to search divorces on-line from 1858 to 1911.
For records 1858-1937 you can search for references to divorce court files at:
http://www.nationalarchives.gov.uk/records/looking-for-perso...I found one family divorce there giving file [number], Appellant [name], Respondent [name], Co-respondent [name]. Type [Husband's/Wife's] petition. Also included was a year date and a reference number. Clicking on the link for an undigitised record will allow you to purchase a copy, or to have the records made available to you to view free if you choose to visit National Archives in Kew.