Barney,
The "standard route" on the western side of the London Zone is via Burnham NDB and Ascot.
Useable irrespective of the runways in use at Heathrow. Not above 1,000ft between Burnham and Ascot to separate from Heathrow traffic, should be able to be a bit higher outside that area.
drauk,
Depending exactly where you choose to pull up you may indeed find yourself reasonably close to something larger. I would suggest you only consider this option if it is good VMC and, during the stress of the moment, you are still able to clear visually the area you are climbing into and whilst up there (albeit probably only briefly) are able to continue looking outside because the larger traffic could be coming at you from any direction and at a significantly higher speed.
I wouldn't say don't do it, I would just say think about it carefully.
Heathrow to a certain extent, and probably Thames more so, don't have a massive chunk of airspace to play with their traffic at the lower levels. One unknown aircraft coming into this airspace can, will and does cause significant disruption.
WF.