Marcie, I'd say you're right about the dates, and it could well be Talbot Woods/Ensbury Park kind of area. I grew up in Parham Road (off Columbia Trees Lane) and Glenmoor Road (near the school), so I used to know the area pretty well. I suspect that the tree will no longer be there - as you say, it'd be huge by now, and that front garden doesn't look like it could take such a big tree.
Linda
PS - I'm wondering if it could also be Richmond Park area. There were a lot of houses built there at around the same time, I think.