Travelling regularly between LHR and SFO, I often look into the idea of "breaking" the journey in the EU en route, especially when the fares seem high. I have yet to find a fare ex-continental Europe that was less than ex-LHR, with one exception earlier this year when it would have been cheaper ex-DUB, by about £50. However, the cost of getting to DUB, and allowing enough time there so as to make sure not to miss by connection, far exceeds the value of £50.