Yes, the Wellcome Library should work for you by email. I am in Canada, and they replied to me by regular post, complete with photocopies, and more information than I really needed to know! The physician I was inquiring about had attended a death of an ancestor, and shared his relatively unusual surname, but, because of the information they sent, I now know that the name was just a coincidence, and that they were not related.
Let us know how you make out. I also have a dentist I want to inquire about, so I will be interested to hear how you get on.