There is a distinction between the recent looting of archaeological sites and the historic removal of sculptures and architectural fragments in the nineteenth century. Debbie Challis has provided a detailed look at British exploration in the Ottoman Empire in the period 1840-1880. This includes the removal of tombs in Lycia by Charles Fellows as well as the sculptures from the Mausoleum of Halikarnassos (the modern Bodrum) by (Sir) Charles Newton. She includes a list of where the objects can be seen (even down to the gallery in the British Museum).
Challis, D. 2008. From the Harpy Tomb to the Wonders of Ephesus: British archaeologists in the Ottoman Empire 1840-1880. London: Duckworth. [WorldCat]