Sometimes the kids' ages and your own personal preferences are a good place to start, especially with such a long time to plan. My friend from high school lives in England and his kids about that age LOVE Lego Land in Windsor. (It does look very nifty) Windsor's also right near Heathrow Airport, and the Castle has a deal that if you have your ticket stamped at the end of the day, you can get back in for free after that. It's also a nice small town feel with good shopping, we found good prices a couple of years ago, and good restaurants too. Thames is right there, and a ferris wheel was there the last 3 times I was there. I found I was more at ease cuz I could know exactly where my daughter was, not as huge as some of the city areas. Good to plan out what phones will really work over there, how to keep the kids connected, safety rules, etc. I've had many phones that were supposed to work over there that did not. I was told my Google Project Fi phone really Will work cuz someone on this forum sent me a message with the details of how great it did work.
The B&B prices will vary with location and quality. There's a big Youth Hostel network that could be a good option in your locations too, I tend to trust businesses, Travelodge.uk and such, and not individual B&B renters. Probably shopping to cook in an air b&b or family hostel could help your budget quite a lot. The Girl Guides and the World Scouting Org also have some hostels in London. You don't have to be a member to stay in them (at least not for Pax Lodge, and I'm pretty sure not for the WOSM property either), might just cost a tiny bit more for non-members. They have the advantage of being set up as kid-friendly, Pax Lodge has a dining hall if you want to buy dinner there, or an upstairs kitchen to be able to prepare your own meals, and nighttime fun events for kids often.
Theatre in the West End is an option for kids too. There's an M&M candy store in Leister Square that was a destination for the volunteers & guests at Pax Lodge.
One of the former managers of Pax Lodge is now working in York at the Train Museum, she loves it and thinks it's very great, so that might be an option if your kids like trains. Pax Lodge is in Hampstead and there's a swimming pond there, and next to Air Studios (where music for Harry Potter and Kung Fu Panda was recorded).
London's got everything and I could stay for years, so things like the boat rides on the Thames could be fun for kids, Trafalgar Square was an instant favorite of my daughter's. There's a huge Imax theatre right next to Waterloo Station, I took her to the last Harry Potter movie there, which had the scene of the dragon coming up out of the glass roof of the station and flying past the London Eye, so we were right THERE for it, in 3D :) . Harry Potter studio has a bus from Victoria Station (and very few other simple options to get to the studio except that couch bus), so you may prefer to be over that way for your day trips, that station has a lot of options with many bus/coach possibilities. I did go on the London Eye but felt it just took me farther away from the sights, but that could be a personal preference. I did it to overcome my fear of heights. :) Also the British Library's Treasure room is great because there's a big variety of fabulous displays, but it's all in one room, comfy benches, can easily see where your kids are, and a little cafe in the building just a few steps away on the same floor. St Pancras hotel right near there is gorgeous, St Pancras station can get you to Paris if you want to take the train, and the King's Cross with Harry Potter gift shop and platform 9 3/4 is there too.
Much of it depends on what you guys love to do and to see. It'll be fun, and tiring :) but just pace yourselves and have fun!
