Much cheaper that way. And you will use it depending on where you stay. The London pass is worth it if you get everything in on the pass. With that said, if you go once, I can almost guarantee you are going to go again. So don’t feel like you need to hit everything.
As has been stated, the museums are free. The Natural History Museum and the Victoria and Albert museum are right next to each other. I love going to Westminster Abbey because of the beauty, history and relatives I have buried in there. In addition, you are right next to Parliment and Big Ben right there.
If you go during the late summer, I highly suggest seeing Buckingham Palace. Some of the castle tours are not worth it...this one is. The Tower of London is also amazing. I thought “the Crown Jewels...meh” before seeing it. I was floored when seeing them and the whole complex has so much history and other awesome things to see.
I haven’t yet been to the Harry Potter Studio with my family, but that is one of the things we plan on doing next time we are there.
London is amazing...one of my favorite places in Europe. With that said, try to get out to the Cotswolds or out to the Dover area and the moors there. As has been said by others, the English country side is amazing and absolutely stunning.