What attractions should I prebook in London?

When are you traveling? This Summer?

Research the days out 2 for 1 although all that's listed might not be offered during your travel dates. You'll have to keep watch.

Churchill War rooms are times entries so that's something to keep in mind as you establish your days itinerary.

British Museum is free.

Pre book the Eye and The Tower of London.

Go to evensong at St Pauls. Can wander after but at least you'll have gotten inside with out having to pay a fortune.

As far as recommending other things I'd say:
Depending on the age of the children, Mudchute Farm
Tower Bridge Experience
London Transport Museum
Museum of London
Natural History Museum
Paddle boats and outdoor theatre in Regents Park
Brick Lane and Spitafields Market
Portobello Road Market
Thames Path
Greenwich
And the Rick Steves London Guidebook

Thanks Claudia.
We will be in London this year, end of June. For the 2 for 1 deal, it seems that a family rate at some places is a very similar price to the 2 for 1. I would assume if we are 2 adults and 2 children they would take off the price of the two child tickets? Am I correct? So from my research St Paul would cost 40pounds if I waited day of to buy using the 2 for 1 and if I book online today it is 41.20 pounds for family ticket. Same situation for Westminster.

I do have and I am using the RS London guidebook.

This is just a tip my brother shared with me that I have to pass along. When you get into the Tower of London complex, go directly to the building that houses the crown jewels. (I think you will receive a map.) Most tourists visit the other buildings as they enter, so everyone converges on the building with the crown jewels at the same time which means a very long line and a quick look see on the conveyor belt. By going there first, you will probably have the place to yourself and you can take the ride past the amazing display twice! We did!

Although I do not know for sure, I suspect the 2-4-1 deals might allow you to pay for one adult and one child and get the second adult and second child entries free. However, that is just my guess, and I think if the cost is fairly similar, it's smarter to buy advance tickets since the 2-4-1 deal puts you in the ordinary ticket-purchasing line. Although my travel mate and I both want to go to the Churchill War Rooms, I doubt that we'll opt for the 2-4-1 offer, because our time is valuable.

From what I've read on this forum, the War Rooms are very, very busy these days, so that's one ticket you'd be better of purchasing in advance.

Aren’t the 2-4-1 passes only for Railways Days Out?

Not necessarily, there are ways around it, buying "decoy" rail tickets or paper travelcards bought at a national rail station.
https://www.tripadvisor.co.uk/Travel-g186338-c133479/London:United-Kingdom:Paper.And.Oyster.Travelcards.2.4.1.Offers.html

I do think that time of year and time of day mpact whether you need to buy tickets in advance. I walked right into the Churchill War Rooms last week. No line, no wait. I’m not sure that would be true for the end of June.

If you’re planning on doing the Harry Potter studio tour, book it, like, yesterday. ;)

For all of the things you list, there is a discount for advance booking. A trick I learned is that the morning you are going is far enough "in advance" unless there are timed tickets. Register now and create an account for any attractions you are thinking of seeing, but not sure enough of to buy tickets now. Then, you can buy tickets that morning on your phone quickly and easily (it's much harder to input all your details a phone than on a computer with a real keyboard!).

For the Churchill War Rooms, these are timed tickets. Definitely book in advance. I'm glad Carol got in easily, but I had a wait of about 30 minutes at 9:45 AM last April. When I got in, there was a very long line behind me, while those with timed tickets had only a short wait. Maybe the increased interest from the movie is waning, but I agree that in June they'll be busier.

As for what else to consider, everyone should be researching on their own. With 7 days, everyone should be able to see their own number one sight, even if it doesn't "send" the others. Remind everyone that they will get a turn for their own "must see."

I like Claudia's list, and just want to emphasize Brick Lane and Spitalfields Market - this is modern London, and is a refreshing change if your family has had enough of "ye olde London." If you don't have access to comparable ones at home, London has a Science Musuem and a humongous Natural History Museum, and these are free.

In addition to the RS book, have everyone look at other guidebooks (raid your library) and YouTube videos. Even though I didn't get the London Pass (it's usually not a good deal), I did find their list of covered attractions very helpful in finding lesser known things to see, like the Jewish Museum and the Museum of Brands, Packaging, and Advertising https://www.londonpass.com/london-attractions/.

And it always has a lot of quirks, but the TripAdvisor listing of attractions can be helpful, particularly once you get past the first few pages of the best known things. Never buy tickets from Tripadvisor - they're just a reseller, and you'll do better going to the source. https://www.tripadvisor.com/Attractions-g186338-Activities-London_England.html

I’d book the Houses or Parliament guided tour in advance although there are often tickets available on the day. It’s usually only on Saturday.