Back in March 2016, I published the preliminary results of research in to the offshore interests of the Buccleuch family. Due to my election as an MSP in May 2016, I have had no time to complete this work but thanks to the International Consortium of Investigative Journalists publication of the Paradise Papers, we now have one more piece of the jigsaw. The jigsaw being who is the beneficial owner of the shares of Bucleuch estates Ltd.)
Kirkhope Holdings Ltd. (larger version of the above image here) appears to be one strong candidate for the entity that holds the wealth of the Buccleuch family. It was incorporated in the Cayman Islands on 10 July 1987 and shares are owned by Buccleuch Estates Ltd. and members of the Buccleuch family.
Over to whoever wishes to follow this up further.