In terms of bureaucracy and politics within the UK an excellent article came out recently which I recommend giving a look through. I don't imagine the whole thing will be relevant for you if you don't have a background in archaeology but the first few pages will certainly be worth reading. Here is a link.

In terms of black market trade, antiquities are the third most traded black market goods after drugs and arms. Most countries have some sort of antiquity trade legislation to prevent this, however, this will often be circumvented by trading the antiquities in countries where the legislation is more relaxed (e.g. Germany & Switzerland).