Some of the manuscripts in the indirect tradition are held by the Wellcome Library itself. I didn't have the nerve to ask to see them, and time was short anyway. However, the Wellcome is, among other things, an educational charity, and I think if a group of interested people requested in advance to see them, the Wellcome would probably oblige. Something for a list meeting in London to do?
The Wellcome Library is also within walking distance of John Dee's magic mirror at the British Museum.