First Day in London with Jet lagged kids!

Would the Thames Clippers/Uber boat interest you. There are regular frequent services from many central piers a long way west and east as far as the suburb of Barking.
Between Greenwich and Barking is also Woolwich Arsenal- now a very well done Museum, a lot of which is outside, the outside bits at least are free. Lots of eating places there.
At North Greenwich you could take the cable car across the river (oyster can be used both on the Clippers and the Cable Car).
At Greenwich there is the Cutty Sark, the National Maritime Museum and the Greenwich Meridian.
There are also conventional tour boats you can take.
And boat trips as far as Hampton Court Palace- you don't have to go into the Palace- then return by train. That passes Kew Gardens- another option.
So you would get largely relaxing fresh air, and on the cable car, a great view over the East end of the Thames, docklands and on a good day into Central London.
The Clippers move at high speed, and it's a thrilling ride, even if a commuter boat. They also sell hop on hop off rover tickets.
Sorry I don't have children, so don't know if any of this would interest you.

I would try to avoid anything requiring sitting for any length of time : it's an open invitation to doze off. The HoHo bus mostly gives you a view of the congested traffic in central London. The Thames boats are great for getting from one place to another for some things, but again, there's the doze factor, and you will have already been the victim of looooong hours of sitting on the plane. Your idea of the London Eye might be very enjoyable for the kids, as long as the weather is favorable. And Rick has a guided walk in the guidebook that goes from Parliament/Westminster Abbey to Trafalger Square that is both interesting and an easy walk.

You won't be starting any of this before late morning, so doing these, plus a stop for lunch, and then a later light snack/drink, should occupy your day until you can access your accommodations.

I wouldn’t be worried about those ages at all unless you have extraordinary circumstances they’ll be fine. But you’ll all be tired and “off” to be sure.

I think London eye is a good idea, maybe a picnic in a park, some walking and shopping, leisurely lunch? Basically be outside but be low key and mellow vs MORE transport time (such as bus ride) or anything requiring super ton of focus.

Anything that involves prolonged sitting, whether it's the HoHo bus or a riverboat excursion, will simply wind up being one of the most expensive naps you've ever taken.
Stay on your feet as much as possible until check-in and then play it by ear. A shower and a change of clothes might invigorate everyone enough to power thru the rest of the day, while a short power nap after lunch may be order depending on how everyone's feeling.

My kids are younger than yours (10 and 7), but I was thinking of going to the zoo on our first afternoon. What day do you arrive? If it's a Saturday, would they like going to the Portobello Market? That had also been on my list, but pictures made it look a bit too crowded for us. But teens might enjoy it.

find a park and do some activity? I've watched vlogs about the eye and it moves quite slowly and takes quite some time, so people might start nodding off. Rick has a section in his book about kiddies.

I mentioned that Hannah R. went to the Tower Bridge and it looked to me like they have stuff that might appeal to kids. Also look for similar vlogs.

https://www.youtube.com/watch?v=-CF9OoQejD0

I find the key to keeping kids from meltdown is to feed them, early and often.

With a 7:15 am arrival, by the time you get through passport control and travel into London ( what is your plan for that?) it might be time for a nice breakfast, along with your walk.

One option would be to walk through Hyde Park to the Serpentine (the large lake in the park) and have breakfast at the Serpentine Bar and Kitchen. Hereis the website:

https://www.royalparks.org.uk/parks/hyde-park/food-and-drink/serpentine-bar-and-kitchen

You can see the menu here:

https://www.royalparks.org.uk/__data/assets/pdf_file/0008/153899/SBK_Breakfast_and_Lunch_menu_Nov_22_web.pdf

Another option would be to head toward Westminster Abbey/Elizabeth Tower (Aka Big Ben) and after admiring those beautiful buildings, you cross Westminster Bridge and turn left on the pedestrian Thames Path, past the London Eye. There are restaurant options along the path, one of which is Giraffe:

https://www.giraffe.net/restaurants/southbank

Here is their breakfast menu:

https://www.giraffe.net/assets/newmenus/Giraffe_Breakfast-Menu.pdf

Afterwards, you could ride the London Eye (book in advance or wait in line) and/or walk the Thames Path eastward as far as you like, then ride a Thames Clipper ( now named Uber boats) back to Westminster.

You will need to figure out a luggage storage place and head there first, of course. Where is your lodging located? You may or may not want to be close to that.

What month?

Where are you staying?

Been traveling to London for decades so if you’ll share intel I’d be happy to suggest a plan A & B.

As others have said stay outside as it allows your senses to adjust. Make sure everyone is dressed appropriately ( by that I mean they are comfortable).

Allison, our then-18 yr old daughter requested that we go to the zoo in Dec 2014. We loved it-the days of the British Empire were reflected in their having some animals we haven't seen in American zoos.

These are great suggestions! I, too, was a little worried about doing anything that would involve sitting and then inevitable sleeping! Claudia, we're staying near Victoria the end of June into the beginning of July. I'm super comfortable on the Tube, so jumping around isn't a problem. I wondered, also, since the London Eye might induce some unwanted naps if trying the Sky Garden would be a better option to catch the view? I had the thought of doing part of Rick's Westminster walking tour. I'd thought one of the Changing of the Guards walking tours would be fun, but you have to meet at 10:15 and that's just cutting it too short.

Ok got it.

First, once through immigration how are you getting into London and then to your Victoria neighborhood accommodation? Tube? New Elizabeth Line? Taxi? Heathrow Express? Asking simply because I would think the kids would find the tube fascinating especially if you don’t live in a city with a subway system.

Once you’ve stored your luggage at your accommodation here’s a few options to consider:

First, ask everyone if they need food. If the answer is yes, head to a pub. Good ones in the Victoria neighborhood are:

Bag O Nails
The Colonies
The Duke of York
Cask and Glass
The Shakespeare

All serve food.

If hungry but want to see things locate a Pret A Manger. It’s where you can get sandwiches and crisps and drinks to take away.

Start walking towards Buckingham Palace and The Victoria Memorial. Walk into adjacent St James park and find a bench to enjoy your take away. Once fed start walking towards Parliament Square. Hopefully the Big Ben bell will toll. You could then walk across Westminster Bridge, or walk along the Thames path or walk up Whitehall enroute to Trafalgar Square.

All these options will allow their senses to adapt.

Pick up a picnic and head for Hyde Park. Rest, eat, stretch and explore.

Going for spring break and our kids are the same age. We also land at 7:15am and our hotel is next to St Paul. So we will drop our bags off and then head over to St Paul Cathedral, then head over to Covent Gardens for lunch, check out Neals Yard/ Goodwin Ct, then head over to Trafalgar Square and head into the National Gallery for a bit maybe 2hrs if we have time or want to. Grab dinner and then head back to hotel. Trying to walk/tube everywhere and stay outside as much as we can