True, but unfortunately for many dates, it is impossible to find a flight to London that is compatible with catching the flight to SF, since there are many days where a direct flight is not available, or is available at the wrong time. Moreover if it's not the same company and you miss the London->SF one, you are going to totally lose the money and need to book a new flight, which is very bad given the cost :-)
However what I can do next time is to go in London a couple days before, meet some people there or just have some fun if it's weekend, and then go to SF.
If you talk to a travel agent they might be able to have several flights on different carriers on the same ticket, avoiding the problem of having to buy the second flight if the first one has an issue.
Through Switzerland or Germany it might be easier than London.
However what I can do next time is to go in London a couple days before, meet some people there or just have some fun if it's weekend, and then go to SF.