Estimate number of traffic lights in a London

Anyone willing to share his/her approach to the above question?

This is my approach:

1) Assume a reasonable geographical area of London in km^2.

2) Model London as a square city.

3) Estimate number of horizontal and vertical streets by assigning a uniform length for these streets.

4) Estimate number of intersections and subsequently number of traffic lights.

But this approach assumes that the entire area is occupied by streets. Would that be a fair assumption to make in an interview?

My second approach would be to assign a percentage of land covered by streets by calculating the percentage of land covered by buildings in London. So I could calculate the number of buildings via the number of households in London (given each building on average holds 10 household). Then multiply number of buildings by 200-300 m^2 in area, to get total area covered by buildings. I could add 20-30% to take into account non-residential buildings, parks, unused land etc. By doing this, i can estimate the area of land covered by streets then include it in my first approach. Or would this be to much during an interview?