Were those original residents pushed out? It seems that in most cases, they chose to move because through moving out to the Home Counties, they could afford to buy a house and garden, or because they wanted the cleaner air and quieter lifestyle. In people I've known who moved out of Tottenham (most of dad's side of family...he was the only one who stayed in N London) there was an element of choice, rather than with gentrification which just makes it actually impossible to afford to live somewhere anymore.Thing is with gentrification is it just another process, most of the originally population of Tottenham and many parts of London where pushed out to the home counties after the war and in their place immigrants from the Caribbean, Indian-sub continent and even close to home like Ireland came in.
Now these second or third generation people are being pushed out probably by the hipster grandchildren of many of the original Londoners sent off to the counties in the first place. Tottenham will survive although to see it become trendy is odd.
As mentioned, some of the descendants of those residents didn't leave, you can still see them around Tottenham and especially in certain pubs on non-match days.