Now if Heathrow Airport Limited were making a case for both a third and a fourth rwy.......
Actually they do, sort of:
"We believe Heathrow can accommodate four runways successfully if required to do so and that the impacts of such a plan can be successfully mitigated."
In fact the proposal illustrates three different four-runway options (plus the Policy Exchange proposal, which they dismiss):
A. north + southwest
B. northwest + southwest
and, you will be pleased to hear
C. dual northwest
Although HAL agree with my assessment that you can't fit two runways
between the A4 and M4 - the northernmost runway runs along the line of the M4, which would now run in a tunnel underneath it.