Passes or Combination tickets - your opinion

The British Museum is free.

I'm unfamiliar with English passes, but here's how you make a decision on whether to get one or not (this applies to any country).

Step 1: Make a list of all the sites you really want to see (and realistically have time to see) during your trip. I assume that the list in your post is your final list?
Step 2: Next to each museum/site, jot down the entry fee of each site (some may be free). This is all best done on a spreadsheet like Excel.
Step 3: Add up all the fees to get a sum total.
Step 4: Compare cost of each pass to the sum of individual tickets. If pass cost < sum cost of individual tickets, then get the pass. If the reverse, then buy the tickets individually. Make sure that each pass/combo tickets you're looking for includes each site you plan on visiting. If not, you need to add any extra costs (of sites that are not included) to the cost of the pass.

The one pitfall you should consider is that people tend to overestimate the number of sites they can see during their visit. So they end up paying for a pass that's more expensive than had they bought individual tickets. That's how these passes tend to make money. So be realistic in your estimates. Only buy the pass if you are fairly sure that it makes sense financially, and make sure it's a legitimate pass and not some scam with too many restrictions (or whatever is the case).

Thanks Agnes. Great suggestion.

A. Craven,
Thanks for the reminder that the British Museum is free. I knew that a few weeks ago, but had forgotten. haha.

What about the 2for1 offers? Directions on the way to do it correctly are here https://www.tripadvisor.com/Travel-g186338-c195600/London:United-Kingdom:2.4.1.Travelcards.Step.By.Step.html

Hopefully others will add on here as I've seen posts that show that the train tickets are a little more restricted to area of the attraction now, but I have no first hand knowledge.

Is this for one person, or are you traveling as a couple?

If a couple, the 2 for 1 offers are rather good, but not so if you're by yourself. In that case, have a look at HRP membership to get you into the Tower, Hampton Court Palace, and Kensington Palace. When are you coming? There's an exhibition opening soon of Diana's dresses at KP.

I would take a good look at what is free around London.
That would include most of the museums.

For example, the excellent British Museum is free.
You could spend three entire days there and still not see everything.

Free:
The Victoria and Albert Museum (V&A)--terrific
The Museum of London--terrific
The Museum of Natural History
The Science Museum
The Tate Modern
The National Gallery
The National Portrait Gallery
just to name a few free museums; there are more.

You will also want to walk through some of London's parks (free).
Take several walks along the river to admire the sights (free).

Keep in mind that a great deal of your time in London might be taken up with doing things that are free.

The best paying sights on your list are:
Westminster Abbey
The Tower of London
St Paul's Cathedral
Windsor Castle
Hampton Court Palace
Kensington Palace

I would do some of the free sights first--the British Museum, for example.
And then decide which of the paying attractions looked the best to you personally.
Maybe do them individually until you run out of time--and you will.

I usually would not recommend this, but since you asked for a pass that is not bogus, here's the London Pass.
https://www.londonpass.com/visitlondon.php?aid=1
This was found on the following page which is the Visit London website, which may also be useful to you:
http://www.visitlondon.com/discover-london?ref=nav#7ixI4Y5o6GQgTG5I.97

Which do you think are not legitimate? I have never heard of any fake passes.

The London Pass is genuine, but is rarely deemed to be good value. Almost every city in Europe has a similar pass and I haven't found any that prove to be good value for what I wanted to see.

Work out what you want to see vs what is free/discounted on the Pass and do the maths. Be realistic about what you can achieve each day - as already been stated, you will need 6 days+ to cover these. Also check out the free museums and galleries.