The revelation that the Matrix films and games take place in a single megacity was surprising, as there were several references to other places and cultures throughout the series. This gave rise to the speculation that the Matrix contains only one city, wherein the names, media, and language differences exist to convince the inhabitants that an entire world exists outside it.
It has never been stated that there is only one location in the Matrix, just that the entire franchise is set in the same unidentified megacity.
Please note that most references to "other" locations (such as Heathrow Airport) mentioned by the original question are merely references - there's no proof that Heathrow was an actual location in the article as opposed to merely a word in an articles that The Matrix generated about Morpheus.
However, some locations seem down as distinct. Again from the Wiki:
The presence of an airport and a post office in Enter the Matrix implies that City-dwellers can travel, or seem to travel, to other cities and countries.
In The Matrix Reloaded, Neo is transported to a remote mountainous area resembling the Alps or the Himalayas (supposedly the location of the Merovingian's mansion), from which he has to fly "500 miles due south" in order to return to the City.
In The Matrix: Path of Neo, Neo, Morpheus, and the Keymaker enter the United States Congress, which is then overwritten by Smith. The presence of a national government suggests that there are other nations within the Matrix.
In Beyond, one of the short films from The Animatrix, the setting appears to be that of Japan - East Asian lettering can be seen on signposts, and the main character Yoko owns a cat called Yuki, indicatively Japanese names. In addition, in World Record, another Animatrix short, the runner wears running gear emblazoned with 'USA', and a nurse mentions her aunt who lives in the south of France. This seems to suggest that not only are there regions outside the City, but other nations too, leading to the possibility of the Matrix being larger than previously thought.
The city was designed to represent an amalgam of any number of major cities in the United States during the 1990s; e.g., gray and utilitarian with small pockets of color and entertainment.
According to the films' graphic designer Suzanne Buljan, companies and utilities in the city were uniformly given generic "City" names which are seen on signage and vehicles throughout the films, such as City Metro, City Waste, City Rail, City Post and City Power:
"Everything is City—something; all the facilities are City related." —Suzanne Buljan
(src: Interview: Suzanne Buljan, whatisthematrix.com)
As far as physical shoot locations, the Wiki states that the Mega City related scenes were based on:
- Sydney, Australia (where most of the movies were filmed)
- Oakland, California (where some of the car chase scenes in The Matrix Reloaded were filmed)
- Chicago, Illinois (where the Wachowski brothers were born and raised)