CoinsWeekly reports on the 150th Anniversary of the British Museum Coin Cabinet here:
http://www.coinsweekly.com/en/News/4?&id=460
At its formation in 1753, the BM was given 20,000 ancient coins. A separate cabinet was formed in 1861. The collection was part of the Department of Manuscripts and then Antiquities before a separate Department of Coins and Medals was set up.
In any event, this again underscores the fact that ancient coins have been actively collected for generations, and that one cannot reasonably assume that an old coin is the product of a recent illicit dig.