Planning your time in London
(work in progress)
Maybe I'm biased, but I really don't think that you need to do a guided tour in London except if you are on a really tight itinerary. There is lots of tourist information available - sometimes too much, which can be confusing - but once you've got your A-Z (streetfinder) and have got the hang of the public transport system, you'll find it far more rewarding and cost effective to do it yourself. If you doubt that you have the confidence to put together an itinerary, then why not find some itineraries offered by tour operators whose focus appeals to you and then duplicate this yourself at a fraction of the cost?
For those who are not used to planning itineraries for large cities for themselves, I would suggest that the key is to be realistic in what you're trying to see. There is no better way to spoil a trip than to micromanage every last minute and get so obsessed to keeping up with your unrealistic itinerary that you don't have time to enjoy what you are seeing. Much of the attraction of historic cities such as London is to appreciate the sense of place/history/antiquity, and this is something that requires both time and peace of mind. Unless you're planning to stay in London a month or more, you might as well accept that you won't see it properly in one visit, and anyway, even if you did, by the end of that time, you'd probably have long since got past the point of sensory overload.
Another good tip is to try and aim for diversity in your schedule. Although similar types of attractions tend to be grouped in certain geographical areas (for example, museums in South Kensington, Wren churches in the City, shopping along Oxford Street), after a few hours on a particular theme, you'll be all 'museumed/churched/shopped out' and will need a mental break. A change is as good as a rest, so I would advise you to intersperse museum visits with a stroll in the park, shopping with a theatre performance and so forth.
Just be aware that even Central London is a large and diverse area, so it's best to plan your trip so that you can tackle bite-sized chunks - for example, Kensington one day, Westminster/Whitehall the next. This approach is not only good for your health because you get to exercise - particularly important if you're doing longhaul flights - but also allows to you explore on foot (always the best way to get to know a city).