I stumbled across this plan (http://www.lrta.org/london-Hounslow.html),
involving a tram from Hammersmith to Heathrow along the A4. They say
that it would reduce traffic on the A4 by 20%, however I understand it
would take up one lane in each direction (33%) of the road capacity,
therefore *increasing* congestion.

I looked on alwaystouchout and I couldn't find the project!

There's also a Heathrow-Kingston tram mentioned too.