I think an approach not linked to population might work better. 

I would approximate London with 3 squares with perpendicular roads. THe numbers are very first guess and you might plug in different ones, but directionally should be OK:

• An inner square with the city, marylebone, vauxhaull, etc...roughly 5x5km. In your approximation of perpedicular roads, you can assume a road every 100m. That gives you 50x50 intersections for that part.
•  A middle square with the outer ring, residential areas, a bit less densly populated, area 15kmx15km, maby a road every 250m, gives you 60x60-20x20 intersections (take out the middle square)
• An outer square with the suburbs, maybe 50x50km, an intersection every 500m, gives you 100x100-30x30 intersections

Note that now you'll still need to apply a discount factor, as not every intersection has traffic lights. Many of them have either a roundabout or no structure at all.