When planning your London trip access a London Underground map and bookmark (or print) it. Search hotels, B&Bs, etc. and list their information on a word processing sheet. Make sure you include the nearest Tube Station for each lodging. On another word processing sheet write out the pertinent information for ALL the things in London you MIGHT be interested in. Include days they're closed, times, and nearest Tube Station. At this point you could have 5, 8 or more pages of things that interest you. That's o.k. for now.
When you've noted all the sites that interest you, rearrange them according to their Tube Station location. Do the same thing for your lodgings Organizing your things in this way groups the sites that interest you together. Then you can see if there are any lodgings near these sites. Work up a short questionnaire for the lodgings that interest you and send the SAME questions to each place. The ones that respond go on your "short list" the ones that don't get dumped. I've found this method of winnowing out possible lodgings works well. Hope it works for you.
I know you want to see/do EVERYTHING while you are there but don't fall into that trap. Plan on doing/seeing just 2 main things each day and keep your sightseeing in the same area so you don't waste time running around the city (that's why you group things by Tube Station proximity). The museums in London are unbelievable and all have great websites. Again, I encourage you to explore their websites and find 3 to 5 really special things you want to see in each museum. Those things will stay in your memory whereas if you wander the museum so you can see everything -- it all becomes a blur and nothing will be special.
Try to start your planning 3 to 4 months ahead of time so that you'll have plenty of time to build the list of things you want to see, allow that list to 'rest' for a bit then return to it. It's much easier to winnow the list to the things you Truly Want To See if you give yourself time to revisit the list a couple of times
Good Luck.