I've done a bit of work tracing London residences for various family members back to about 1860. It can be tricky as the numbering has altered in some areas. I don't know of a definitive source that lists the old numbers.
My advice would be to check out as many of the old maps (as others have listed) to get an idea of the areas, then compare to the modern map. Also take advantage of Google Streetview which is a cheap way of checking out the modern site. You can immediately see whether the building has been replaced with something more modern. Bombing has altered some areas quite significantly and I there is a map which shows the areas that suffered bomb damage to varying degrees. Other areas were once dense slums or narrow streets which have been cleared away. A lot of the old alley networks are gone, or remain in part.
Also, try and read as much of you can on the history of the areas you're interested in. There's some smashing contemporary accounts, some online. It's worth doing a lot of Googling.
Finally, if you can, I recommend tracing it all on the ground, on foot ideally. It's a great way to get a feel for the areas and even if the exact building can't be identified, or has gone completely, there's often an old building nearby which your ancestors must have known. Seeing what they saw is a great way to connect.
Hope this is helpful.
Regards,
Mark
