We got our reply (emphasis added):
Thank you for your recent telephone call to the NHSBT Donor Line.
I can confirm that Scottish independence will not affect organ donation and the system will continue as it does currently.
I hope this answers your query, please let me know if you require any further information and I will be happy to help.
NHS Blood and Transplant
Organ Donation and Transplantation Directorate
Fox Den Road
Tom didn’t actually say the words “Gordon Brown is lying through his teeth to terrify Scottish people into voting No”, but we think it’s pretty much implied.