Aside from a pamphlet showing the routes, Heathrow actually does little for the cyclist - probably because they can't find a way to make money out of us.
The problem with cycling is that the money is never a
direct financial benefit, so anything that helps us out comes via planning bribes or greenwash policy statement.
At an airport we have an
additional problem that very few people will actually cycle to the airport to catch a flight - and that's the same even at airports in cities with very high cycling rates (AMS, CPH etc). You just don't stuff a 23kg suitcase in your panniers, and even if you're going on a cycling holiday, chances are bike goes in a box, then car or taxi to airport.
So that's why cycling has been brought up in the context of R3. Reading through the TfL document, together with known policies of the 3 main parties, there is a widely held view that the air and noise pollution problems around LHR make the idea of a 3rd runway
impossible.
This then gets countered back with all the economic arguments about why LHR R3 is the
only option, and why doing nothing is also
not on the menu.
So they only way to break the stalemate is a
significant reduction in local air pollution, the
majority of which is caused by road vehicles.
You can't take out the through traffic very easily, nor can you do much to discourage people from driving to the airport - for example, if the airport were made to raise parking charges, the off-site operators would just cash in.
So the only real hope to get this through is a
significant reduction in local traffic, and that includes staff movements to and from the site. Some of this will come through bus and rail improvements, but these are all very capital intensive. Hence, the cycling schemes can
help towards the case for a third runway, and they are the
cheapest way of doing so.