How can my family make the most of our trip to London?

I highly recommend the The British Museum and the Tower Of London. Both are fun and educational. The tour at the Tower of London was really fun. Save the British Museum for a rainy day, you and easily spend 4 hours there, and kids will love it.

Visit Olympic Park and take your children to the swimming pool, is a beautiful building and part of the recent history of London, also if they are up for a ride take them to the bmx experience is awesome!

Just wanted to thank everyone for all the helpful answers! We had a great time. We tried to see as much as possible, but looks like we will need a couple more trips. Four days just wasn't enough time!

You will probably get the best value for money for central London accommodation by looking south of the river in the Southwark area. It is still close to everything with good transport, but does not have the premium of West London or the city. You may also want to consider getting an  apartment, as this will give you a bit of freedom and you can save money by doing your own thing for breakfast etc. There is a great food market called Borough Market near London Bridge station, so you can enjoy the foodie part of London there and have simple, cheap, fun getting some great foods.  

Get Oyster cards and travel around on the Underground. It is easy but not cheap. As you are from Holland you may want to use the Boris Bikes that are available for rent around the city. The tfl.gov.uk site will give you information on these and the Oyster Cards. 

Most museums and galleries are free in London, so that is a great way to go. Depending on the interests of your group, the V&A, British Mueum, Science Museum, Natural History Museum and the Museum of London are all worth considering. Greenwich is a great day out, with lots of things for everyone. The Tower of London is a must and St Paul's is well worth the time as well.

Definately see a show. For your group, Matilda or Wicked could be good, depending on what you like. There are lots of places around town where you can get 'half price' tickets on the day of the show but try to avoid Friday and Saturday nights. 

It is a great city with lots to do. The timeout website has loads of stuff on it too. Have a great time. 

If possible I stay in Hampstead Village with my daughters. It's like a village within London and can offer a respite for the hurly burly of the city. Plus the views from Parliament Hill of the cityscape below are beautiful. Try the eccentric but charming Hampstead Guesthouse for some rooms. 

The The British Museum is free and chock full of stunning exhibits as is the Natural History Museum (although this has a fee). Read up beforehand and take in what you really want to see otherwise you'll quickly become overwhelmed. The 'picture postcard' event of the changing of the guard at Buckingham Palace often goes down well but I'd avoid any west end shopping streets such as Bond, Oxford and Regent street. Nothing but crowds and familiar brands. 

If it's fine weather a walk in Hyde Park and the playground in Kensington Gardens can while away some time. As can a stroll along the south bank - start from the Millennium Bridge and the Tate Modern (free) and head down past the National Theatre. 

The Monument to the Great Fire of London is often missed but very cheap at around 3 pounds. Walk up around 300 steps inside for great views from the city centre. You even get a certificate on the way down. 

Covent Garden is also a great place to wander around on a weekend. Camden Market won't have too much to offer a young family. 

If your children like Harry Potter then I really recommend a day trip to the Harry Potter London Walking Tour a 20 minute train journey away. 

An open top bus tour or a river boat tour - there is a large speedboat that takes in the sites with the expected thrill of speed.

The London Eye needs booking in advance.  

For a big family trip it might be worth renting an apartment or house. London is very well served by public transport: Underground, buses and trains, so you can stay outside the very centre and travel in, if you like. Hotels in London can be quite expensive. You can find nice places on websites like: www.ownersdirect.co.uk or www.holidaylettings.co.uk If you really want to splash out try: www.onefinestay.com It might be worth your while to buy a London Pass which allows free entry into a lot of London attractions www.londonpass.com If you add a travel card you get unlimited public transport travel on underground and buses. A visitor Oyster card is also good value for travel in London. Here's a useful site: www.tfl.gov.uk There's something for everybody in the city - all the popular attractions: Tower Of London, National Gallery, The British Museum, Tate Modern, London Eye, Covent Garden, Buckingham Palace, Oxford St, Regent St, and Bond St, for shopping. Or take in one of the weekend markets like Camden Market (www.camdenmarket.com). If you have time take the train to OxfordIt's a really beautiful small University city an hour outside London. Have a great time.

(view from the cruise down the Thames)

We took our children last spring, they were older than yours, but the only thing they really wanted to do was actually walk around and "see" the city..the negotiating for the trip involved how many museums we could visit! :)! We took the boat ride from the Tate Modern to National Gallery and they really enjoyed that! After all the walking it was a nice change! They also loved the London Eye! Me...not so much!(London eye and Parliament building)

(Me on London eye doing my happy place chant)

just one other quick thought..we did do the tube..once! It was sooo crowded I made my 17 and 20 year olds hold our hands!, we opted for the bus, its less crowded (read less panic for mom!) and you get to see the city, which is why your there, right? .. the Oyster card can be bought and loaded ahead of time and reloaded as you need, we reloaded once in 4 days and still have the majority on it..they don't expire..good luck and have fun!

I agree that you should consider renting a flat or apartment. The East End near the Tower offers some good value and a lot of public transportation options.

Also research what you are interested in and note the location. London covers a lot of area so group together sites in the same area to save travel time, like the Shakespeare's Globe and Tate Modern are close to each other; the Natural History Museum and Victoria & Albert Museum  are across the street from each other; the London Eye is near the House Of Parliament and Big Ben.

A lot of good replies already so I won't re-hash any of the previous suggestions (Though I will correct some wrong information. All major museums in London are free, including the National History Museum. Also to climb the Monument is £4 not £3).

I also disagree that a Visitor Oyster Card is good value. Either a regular Oyster Card or a National Rail Travelcard is better (the latter offers 2-1 tickets to many major London attractions so you get transportation and MUCH better discounts than the Visitor Oyster gives).

Greenwich Park is a good place to visit. The park is nice with great views over the city. You have the Royal Observatory (Home of time and Meridian Line) and the Maritime Greenwich which is a huge (and free) naval museum. If you saw the 2nd Thor movie, the whole end battle was filmed there! Last but not least there is the Cutty Sark, a very old, famous (and pretty) Clipper Ship, though there is a charge to go inside, you can still get some really cool photo's from outside (sorry, despite the peep of blue sky it was a terribly dark and grey day when I was there).

Greenwich is on the Thames Clipper route (river bus), so if you want to ride the boats on the Thames, this is a good way to kill 2 birds with one stone.

A little further along (you'll need to take transportation, too far to walk), is the O2 Arena (aka the Millennium Dome). You may recognise the round, flat-ish buildings from a lot of movies including an older James Bond one who's entire pre-credit start sequence too place in speedboats around it.

You can actually go up on the roof of the The O2 Arena if you are daring, however I'm actually suggesting going there for the Emirates Air Line Greenwich Peninsula Terminal.
 This is a Cable Car that takes you across the Thames and gives great views of the city. As it's a form of public transport it only costs a few pounds each way so is an absolute bargain too. The other side is the Royal Docks, nothing super stunning but ok for a brief wander. On the O2 side there is also the Emirates Aviation Experience which is a museum all about flight and airplanes, if that sort of thing interests you all (there is a charge for this but you can buy a combined museum and cable car ticket for a discount).

Hope that helps :)

Check out a child appropriate play and got to the Tower Of London, they will have a blast! The London Eye is also a neat experience.

Lots of free museums in London, something for everyone's interest.  Depending on the interests in the group, give some thought to splitting up if 1/2 want to go to one place and 1/2 to the other.  We did that when we took our niece and nephew and it worked great.  They both loved the Science Museum, it had a great interactive section for the kids.

The markets are also free, if the 13 year old is a girl she might enjoy Camden Market, Portobello Rd is interesting, Borough Market is an interesting food market.

One place that I take everyone to is the Tower Of London, it's fun, it's got great history and people of all ages like it.  Look for family discounts, the Tower has an online deal where 2 adults and 3 kids pay 57.40£

London is expensive, period.  It's because of the pound.  Think of it this way, the pound buys what a dollar buys here, so if you think $5 is a good price for something here, 5 pounds is good there.  Nothing you can do about that, and if you let it get to you, your trip will be spoiled. That said, here are some tips.  

Stay near a tube stop, preferably on the Circle line.  Buy Oyster Cards with unlimited off-peak tube usage.  It's a bargain compared to cabs, and you'll be able to then go wherever you wish, though I highly recommend walking.  If you stay on the other side of the Thames, you can take some tube lines into central London. To save some money could stay in Paddington, Hotel Indigo London - Paddington is lower priced and not bad and you're right near the train station where you can go anywhere.  Also Hotel Novotel London Paddington is very nice and lower priced than most.  Novotel and Park Plaza hotels are generally better priced and good values in London, and they have plenty of locations.  Honestly, you can stay anywhere along the Circle Line if you're close to a tube station - walking distance is key.  Pro tip, make sure you check the train info, because invariably some parts of the Underground are closed at various times but don't let that stop you, just work around it.  Walking is the best part of being in London of course, but the tube will allow you to maximize your time and get more things in when you need to.  

Go to Sunday Up Market

Spitalfields

Borough Market

Get tickets for plays at either the half-price booth in Leicester Sq. or any of the discount ticket offices in the Sq. and off.  

If you can, and if it's playing, go see Classical Spectacular at the Royal Albert Hall  I know it sounds hokey, but the word spectacular really is appropriate.