From what I can find on the net I'd say its doubtful Harry tufnells father was call Adolphus Tufnell. He had three children, Harry junior, Elsie & Hilda. Elsie died as a teenager and Hilda married, renamed and had children. One of which lists the surviving descendents on a website dedicated to tracing family historys (she gives no names, just sexes) and if her nephew was phil tufnell surely she would have said so. Phil Tufnells father is Alan Tufnell so for his story to check out then Alan Tufnell's father must be Harry Tufnell junior.
Tuffers is now backtracking. It got mentioned again because of a listener's email and he said 'I'm pretty sure there's a link...not sure...but pretty sure'!