I decided to map all the postcodes onto the UK map where more postcodes for a specific place would create a "lighter" colour. Each postcode has on average about 15 addresses, so in more densely populated areas you have more "postcodes-per-area". Doing this wasn't very difficult and it resulted in the following map.
He walks through the entire process including how, in working with the data, he noticed alignment issues caused by the differing projections the map information service uses (Mercator) versus just mapping to a flat image. Some calculations were made to convert the latitude/longitude to the correct locations and the resulting points were plotted on a cut-out image of the UK.
After I figured out all the maths for this, the only problem that remains that implementing those algorithms in PHP is show-calculating all the positions from the 1.6 million postcode locations takes up to 10 minutes. This is why I am not presenting any code yet. I am planning to implement all the necessary calculations in a PHP extension to speed up the calculations.