Hello GloriaF ~
Where to begin? It seems like you have already identified some of the places that you want to see, so that's a good start. So your question seems to be, How do you go about seeing these places?
The very first thing I would suggest--now, while you are home and have time to plan your visit--is to get hold of a good London guide book and familiarize yourself with those sites you wish to visit and their locations. I can't emphasize how helpful it will be for you to get a sense of the overall layout of London--where things are relative to one another, and how to get around from place to place--before you actually arrive. A decent guide book will also introduce you to places you might not yet know about but which, when you read about them, you will decide that you want to visit.
(For starters, take a look at Frommer's London Day by Day. It's a handy little guide book that you can slip into your pocket book, yet contains a wealth of practical information. The contents are well-organized; the book not only includes listings and descriptions of numerous tourist attractions and other places of historical and cultural interest, but also gives helpful suggestions for organizing your time in London, with maps showing suggested walks, among other things.)
Virtually every museum, palace, cathedral, church, historic landmark--you name it--has a website that you will tell you everything you need to know about to help plan your visit. (E.g., location, how to get there, opening hours, admission prices, special events or exhibits, and the like.)
I would also emphasize that you don't need a tour to get to Buckingham Palace or the Tower of London or any other site of interest. Wherever you are staying in central London, you will be able to travel to that site by public transport (Underground or bus) or, if need be, by taxi. And once you have arrived at your destination, you will find that you don't need a tour organized by an outsider. For example, the Tower of London has its own guides--the Yeoman Warders, aka Beefeaters, whose special status as guards and caretakers of the Tower date from Henry VIII. Most historic churches have leaflets detailing the history of that particular church and showing the locations of various points of interest inside the church, and many of the really historically significant churches such as Westminster Abbey have vergers who conduct tours within that church.
I can't do more than begin to scratch the surface here. But once you get a bit of a handle on what you want to see and what you'd like to do during your visit, you can certainly ask more specific questions and get more detailed advice from locals and experienced travelers alike.
(For what it's worth, I'm an American gent of a certain age who first stepped foot in London as a child in the mid-1960s. Over the past half-century, as an adult [allegedly😉], I've visited more times than I can count, and have lived there for extended periods. And even after all this time, there are still places in London that I have yet to visit.)
Hope this helps.