Do the addresses on your ancestors' letters still exist as homes or businesses today? Do they reflect differences or similarities between the social class of the sender and of the recipient?
You can check whether old addresses still exist by visiting www.royalmail.com. But be careful, houses in a street may have been renumbered and streets might have been renamed.
You might also look at local maps online or at historical maps of the locality in local libraries.
See Local maps in the National Archives UK
Trade directories for local areas can tell you for what purposes buildings might have used in the past and, in some cases, who might have lived and worked in them.
Historic Trade Directories held by Leicester University
Postcodes did not exist at the time the first national British Postal Service started (ie 1840). They were developed gradually over the 1850s and 1860s, starting in London. But, they were not as long and complex as they are today. In fact, the type of postcodes with which we are familiar did not come about until 1974.
More Information on Postal Heritage UK