My first suggestion concerns your transport from Heathrow into the city. I would consider taking either the Heathrow Connect (cheaper/slower) or Heathrow Express (more expensive but faster). Both go to Paddington where you can transfer to other tube lines. Both these options are MUCH faster than taking a bus into the city...
I love Kew Gardens and we spent the better part of a day there. It is immense, ~300 acres, and contains an older royal palace. There is a lot to see but keep in mind that tube trip is almost an hour from Kensington area (depending on tube changes, etc.) It's probably not something you can do in an afternoon if you plan on seeing other venues.
I have been on the double-decker tour bus circuits and found them only marginally helpful in getting the lay of the land. The traffic in London is horrible. Your timing suggests you'll be getting on one during the evening rush so you can expect to be sitting in traffic more than actually moving. I would save the money on this one. A better option might be to take an evening Thames River cruise...
Check the travel times to Hampton Court Palace using the Transport for London web site (or Google/Bing Maps). You might determine it's too logistically difficult to see on the same day as another major venue.
Do you plan on touring Buckingham Palace to just doing the walk-by. If you want to tour it, purchase your tickets in advance so you have control over the day/time. If you only want to do a walk-by, I also suggest the Royal Mews (right around the corner) and the Guards Museum. If you plan to observe the changing of the guard (I haven't compared their schedule to your itinerary), I suggest visiting the Guards Museum first thing and then watching the guards form up (guard mount) next door and then following them down Birdcage Walk as they march to the palace. Chances are, unless you get to the palace gates obscenely early and camp-out, you won't be able to see the actually changing of the guard anyway (throngs of people arrive hours early to get their spot).
I’m not sure I understand why you are using a tour to visit the British Museum – it’s free and the galleries exhibits are very well documented. BTW – I have been to some pretty big museums but this place tops them all. We were there for half a day and only scratched the surface. My suggestion, get on their web site and plan out which galleries interest you the most. You can’t see the entire place in one day so don’t even try.
Portobello Market was a great experience but if you're a foodie, Borough Market is the place to go. Borough Market pairs up well with St Paul’s because there is a bus line running between the two. Either way, plan on getting for lunch. (The paella at the Portobello Market was out of this world!)
You might also want to consider the Museum of London – well worth the time.
If you have a functional smart phone (with data plan), the Transport for London (TFL) web site trip planner is indispensable for getting around.
Good luck and have fun.