Piccadilly Line: £2.40 off-peak with Oyster to a Zone 2 station in SW London. Takes damn near 90 minutes, though. Conversely, LGW can be done in around 45 minutes for around £8 on the overland trains.
Going from SW London to LHR via public transport is a pain, which is a shame because it's closer and I'm under the flight-path anyway.