Dont Forget Westminster Abbey, bits of Westminster School and Charterhouse Square and Barts in General.
The present Barts Hospital building dates from 1729 but the original seems to have survived the Great Fire so, presumably, other buildings in that enclave might still remain (not sure when the River Fleet disappeared underground or if it might have played a part during the Great Fire). Those back streets looks olde but I just don’t know how old. Thinking about those streets and Temple, I’d have to say the stonework of them doesn’t appear as old…but I’m not an expert.
I’d agree that one might think bits of Charterhouse Square would fit the bill but seemingly they don’t. http://www.regentquarter.com/Exhibition/siteHistory.htm
Westminster Abbey was well west of the Great Fire – and almost certainly not even in ‘London’ then – and also escaped the attentions of the Luftwaffe. Not sure how evocative of medieval London it is of itself, though.
I thought Westminster School was in a new building in the City so perhaps I don’t know of that to comment.
Westminster School aside, I’m still guessing Temple is the only area that might fit the bill.
This gives you some idea of how far the Great Fire spread.
http://www.channel4.co.uk/history/microsites/H/history/fire/map.html
How far the Temple is actually ‘medieval’ is debatable. The church was very heavily restored in the nineteenth century and almost none of the surrounding buildings date from before the seventeenth century (that they are mostly in brick or stone is indeed the big giveaway). The Middle Temple Hall is the exception, but, as London_Calling has already pointed out, that dates only from 1573.
The Staple Inn is, IIRC, another post-Blitz reconstruction, as is most of the Charterhouse. Bits of Westminster School are medieval (although, again, with some war damage), but it doesn’t feel typically so and, in any case, it’s not usually open to the public. The only pre-eighteenth century bit of St. Bart’s is St. Barthlomew-the-Less and that too had to be extensively repaired after bomb damage.
The best preserved example of a large pre-Fire house is Crosby Hall, but it has been much mucked about with, not least because it has been moved to a completely different location.
http://www.richardiii.net/sites_crosby.htm
Yet, if there is very little of medieval London that survives above ground, an amazing amount has been excavated over the past 60 years. The best place to start to get a sense of what has been lost is the very readable account by the leading expert on the subject, John Schofield’s Medieval London houses (Yale University Press, 1994).
Amusingly, the aforementioned Marais is now the gay village.