Use of definite article before phrases like Heathrow Airport, Hyde Park, Waterloo Station, Edgware Road and Parliament Square
Solution 1:
Alexg has got it right, in my view. However, since OP says he is waiting for someone to provide a generalized answer, here's mine.
It is hardly ever wrong to omit the article. "The Mall" is the name on the signs, so must be used: "Strand" (the formal name) is both awkward and confusing, so 'the Strand' is usual: most English towns have a few similar names.
Otherwise, there are many names that have developed from descriptions; 'London Road' is the classic example. Most towns in the Home Counties have a road that leads towards London, and refer to it as 'the London road'. Often, when street names were being given, it was named "London Road". In such a case, locals will often call it 'the London Road', while outsiders including the Post Office call it 'London Road'; I wouldn't say either was right or wrong. (Road is, in practice, the only term to which this applies: "the High Street" is usual, but so is "Church Lane is the high street in that village.")
Similar rules apply to stations, airports, roundabouts, etc. Bournemouth has a roundabout with a Frizzell office block, which everyone calls "the Frizzell roundabout". The council put up a sign saying "Frizzell Roundabout", so you can call it either. As far as I can see, all names with articles follow this rule: you can call what used to be Eastleigh Airport (the airport for Southampton) either "Southampton Airport" or "the Southampton airport". "The Southampton Airport" is not correct, but is an understandable mistake; if enough people use it, the name will change.
One last purely national point; in theory, you could refer to a railway terminus named 'Thingtown Central' as either "Central Station" or "the Central"; maybe this happens in the US. Britain has too many places like Exeter, where Exeter Central is a suburban halt, and the central station is Exeter St David's. (The explanation is historical.) So "the Central Station" would be highly ambiguous, and is never used.
Solution 2:
These place names are used without "the" in sentences like "My flight is leaving from Heathrow Airport in forty minutes, and I'm only at Waterloo Station".
(The rest of this answer is describing usage in London and the south-east of England, since you are asking about London place names. Usage in other places is different! As Colin Fine points out in the comments below, usage differs even within the UK.)
Sometimes, you can say "the" before the name of a street. This is never compulsory (except in the special cases 4 and 5 below) but it can be done. I do not know that there is a general rule about when this is permissible. I suspect that the guiding principle is that sometimes, the name of the road coincides with the way you would describe it if it had no name - the Edgware road (small r) is a decent way of talking about whichever road goes to Edgware, and so "the Edgware Road" can be used as well.
- "The High Street" seems to work. This may be because "the high street" is a general term for the main street in a town.
- Descriptive road names can take "the", like "the King's Road", "the Strand", or "the Embankment".
- If it's X Road, and X is where the road goes, then you can often say "the X Road." But this probably only works for "Road", not "Street", "Lane", etc.
- Some streets have "the" as part of the name. Example: The Mall. (We never say "I walked along Mall.")
- For motorways and the like, we always say "the", as in "avoid the M25" rather than "avoid M25".
Here is an example, from The War of the Worlds (H. G. Wells, 1898):
There were one or two cartloads of refugees passing along Oxford Street, and several in the Marylebone Road, but so slowly was the news spreading that Regent Street and Portland Place were full of their Sunday-night promenaders ...
Oxford Street leads (eventually) to Oxford, but I have never heard it with "the". Marylebone is a region of London and it's where Marylebone Road is/leads. Regent Street and Portland Place are named after people, and are also not Roads.
Solution 3:
The related question and your own example mention the Advanced programming in Java whitepaper. The article as necessary because the discussion is about the whitepaper and Advanced programming in Java is adjectival, which is my interpretation of Kosmonaut's advice.
But I don't think we can extend the same example to sentences using Heathrow, Hyde Park, or Waterloo.
It's better to think of the proper noun as you would a person's name. Native English speakers don't refer to a person as, for example, the William, although I have heard it done by ESL speakers.
I hope someone can provide a firm rule for this situation. One of my work colleagues has been doing this for the past 35 years.
Solution 4:
"Hyde Park" is is a proper noun so does not use the definite article. However it would be "the Hyde Park fountains".