It might be the ticket office for the Edinburgh Festival!
This site states that St Oran's Church and St Columba's Church merged in 1948 to become Highland Church, which (through subsequent mergers) became Greyfriars Tolbooth and Highland Church:
http://warmemscot.s4....mscot-post-35357.html
The problem is that it's not clear which buildings were lost and which remain, but it seems certain that the successor church can now sell you a ticket to a show!
http://www.raymonddeg...om/photo_6562041.html
So the building you're seeking is either that one or it was located somewhere close by.
Try an email to Edinburgh City Archives:
[email protected]
OR . . .
If you can get to Edinburgh City Library, head for the Edinburgh & Scottish Collection. They've got two copies of
"Ceud bliadhna, a hundred years, being the centenary review of Edinburgh Highland Church, St Columba's and St Oran's, 1851-1951", shelved at BR 5346 C72 in the Adult Reference section.
Location and contact details here:
http://www.edinburgh....d_scottish_collection
Chris