globetrotter,
When you say 4, I take it you exclude LCY and SEN?
Problem is, the rail network is built around major stations, essentially in and out of central London. There is direct FCC LGW-LTN service, but largely by accident of the Thameslink project, not a specific plan to link them.
There are certain elements of the rail orbital you talk of planned by TfL, but not on the scale you suggest, again the cost would be billions.
Also, most traffic at STN and LTN is point to point, so is a good chunk at LGW - the high value, high yield stuff goes through LHR anyway, so it will always be cheaper to let the others take buses.
As for simple rail improvements at London airports? A spur to LTN? And why oh why was £1.8bn spent on a mile or two tunneling into LHR, but not 'left turn' to the major rail junction of Reading provided?