My childrens Great Grandmother was born at Silver Lion Court Poplar in 1902, it was very very overcrowded then, and so probably alot worse in the 1920s. By then they hade moved to Stepney.
What do you know about Vera? When you say she may have eloped, do you think she actually married the man? Was the man free to marry? maybe they just moved somewhere they were not known and lived together. What was his occupation? Was he a travelling person or did he have family? Your info must be based on a family story and so maybe various members know bits of the story. One thing is for sure, Vera is going to be dead now, and so the death indexes may be a good place to search. The informant at the death will have had to provide the place of birth and this will have cross checked. If you have a surname for the man, that may be where to start. There is a way of finding out info but it is not easy, all you need is someones's name and date of birth and the National Insurance can usually tell if they recieved a state pension in this country, and if so when it stopped, but I have not used those archives and so I am not sure how accessible they are.
I would try to speak to your older living relatives who may be sitting on some information. (Is there a possibility that this aunt left a child behind when she left? )