1. You can get to your destination in a comfortable fast train.
Unlike travelling by car - where the kids are strapped in at all times - or by plane - where children need to be strapped part-time- , a train provides more room to sit and more freedom to walk around. If you are lucky, you get 3 or 4 chairs that face each other and then you have your own little family department.
For toddlers that are very often still very fascinated by public transport, the fact of being on a high speed train is a great adventure. As a potential bonus it even rides in a big tunnel under the sea!
At any moment you can go to the toilet, there's a changing table on board and there is a bar to provide cookies, snacks, drinks, ... In first class you are served a meal similar as in a plane. In the Eurostar you can order a kid's meal but it's a mystery what the difference is between that menu and the normal version. You can't blame them to offer a stereotype kid's meal.
2. Most is stroller accessible:
Walking around through the city with a stroller in London is very different to walking with a stroller in Belgium (when I take Leuven as reference at least). The sidewalks in London are wide and each cross section with a road has a nice slope so walking with strollers is very easy. Attractions that are not centuries old, also have accessibility ramps, elevators etc.
The newer double deck busses are wheelchair accessible as well as the 'bus' connection on the Thames. And you are authorised to simply roll your stroller in a black cab and get a ride like that without having to worry about having a child seat.
The only difficulty is the Tube: only some selected train stations are wheelchair accessible, so you run the risk of carrying your stroller on multiple sets of chairs if you want to get somewhere via the metro.
3. A great variaty of attractive local transport:
I found London quite walkable before we had children but distances are too long for young children to walk themselves. So either you carry/ push your children, or you combine some toddler walks with the public transport.
For small children, all these new ways of transport are part of the attraction: riding the metro trains in the Tube, taking a water bus, boarding a dubble deck bus, ...
The water bus by the way has a bar inside, very comfortable seating and toilets and it is nicely heated in winter time, so I found that a very nice way of getting from one side of the city to the other side.
I do recommend getting an Oyster card as it makes public transport hassle free.
4. Free musea :
As described before here and here , London is full of high quality well known free musea. A lot of them offer children's activities, but as we experienced not all of them do to the same degree.
But with some research you can surely find several that would match your child's interest for a while (obviously, don't drag them into a museum all day): mummies in the British museum, art in Tate Modern or the National Galleries, dinosaurs in the Natural History Museums (mind the waiting queue's!!), planes etc in the Science Museum, fashion history in Victoria and Albert Museum, ...
They are an easy escape when it's cold or wet outside, but since they are free they can also serve as short visits that create variety in your day's schedules.
5. Snacks toilets everywhere :
The city seems to boast a coffee or snack shop on each corner of the street: EAT., Costa, Starbucks, Pret à manger, Caffee Néro or a local pub always seem to be within a few minutes walk away.
They are very welcome when walking around with toddlers that all of a sudden need to pee, even though 5 minutes before they ensured they surely didn't need to go, or with babies that all of a sudden crave for food. (sidenote: some EAT's or Pret's are so small that they don't offer washrooms). Of course they are a welcome excuse for parents to take a break and sooth the children with a healthy snack.
Unlike the US where children are not allowed in licensed pubs, you can take your children into British pubs and traditional pub food turns out to be quite popular (less healthy) food for children: fried chicken, sausage and mashed potatoes, potato wedges, ...
6. London is filled with parks or traffic free walkways (eg south shore of Thames).
When your children are in need of some room to move freely and use some energy, you can go hunt some squirrels in the parks while you enjoy the green surroundings.
They can walk with you along beautiful sights while you don't need to worry about traffic.
7. It's the city of "cars 2" and "royalty"
Toddler fans of the cars movies will be delighted to walk around among the scenes of Cars2: Tow Mater was hung in Big Ben, the race passed on the Mall and the bomb almost exploded in front of Buckingham Palace!
Toddlers that are really into princesses and princes can also get attracted by all the Royal sites in the city.
So it's quite easy to find angles to introduce the city to your children according to their interests.