We don't have any verifiable statement anywhere in this thread or linked sites that there actually is one in SE1 - all we have is Harry's original post that he had heard there was one "on the South Bank".
An article, which happened to be published in "In SE1" states that there are two in Southwark, but does not give a source other than directing us to the website of the Letter Box Study Group.
From a post I have found in the Greater London Industrial Archaeological Society Newsletter in 2002, it appears that one of these could be in Nunhead Lane SE15.
From what I have now discovered of letter box history, and what I know of Southwark's building history, I suspect that the box is close to an area that was new residential development in 1936.
This makes me suspect that if we are to find the letter box in north Southwark, we should concentrate our search on the LCC estates built off Rotherhithe Street in the mid 1930s.
Edited 1 times. Last edit at 19 January 2005 4.17pm by Lang Rabbie.
Narrowing the search down a bit and off at a slight tangent, the phone box at the side of the Roebuck in Trinity St. was listed by english heritage in 1972 "Telephone kiosk. 1927 by Giles Gilbert Scott. Cast iron. Type K2 with domed roof" The post box in Trinity Church Sq I think is also listed - perhaps this is the rare box you seek?
having queried the Listed building service data, it would appear that there are only 3 listed letter boxes in Greater London. None of which are south of the river, and none of which dat from after mid 19th Century. So it would appear that it is not listed.
I will however attempt a different type of search and see what results I get.