IIRC, the last time I read about this idea, was for Northolt to be the UK domestic terminal. So if folks were just coming down from the North to London, then straight into town on A40 or the Central Line etc. If needing to Hub, then express above/below link into the central area.
If just serving as Domestic or other SH to near neighbouring places like AMS etc, then the runway might suffice?
That's why I think it makes sense as a kind of La Guardia - only not as close to the City !
If you wanted to extend SW, then you have to drop the A40 and a railway line into tunnels, if you tried to expand NE then you start ploughing houses.
That's why I think it will not happen.