Thinking back to my student days at The London Hospital in Whitechapel, The pub most used by students (other than the students' union bars) was The Good Samaritan: an appropriate enough name for a pub sandwiched between various hospital and medical college buildings.
After you graduated, it was more likely you would go to "The Grave Maurice" - just over the road near Whitechapel tube station. There was a code for this, when speaking in front of patients - "See you in the chapel later" - so the patients assumed their junior doctors were all religious....?
"The Grave Maurice" and "The Blind Beggar" were both frequented by the Kray brothers, and indeed the murder of Cornell by Ronnie Kray took place during my time at medical school. Some info about these 2 pubs and the goings on there in this article:
Pubs with a secret history