2 young kids, 2 adults - London hotels?

Try https://www.premierinn.com/gb/en/why/family.html

Yep Premier Inn rooms sleep 2 adults and 2 children and are very good value for money for families. Kids eat breakfast free with a paying adult.

Different country different way of life.

They drive on opposite side of the road, allow children in pubs, call gas stations petrol stations, call potato chips crisps and have a King.

As noted try the Premier Inn chain.

Also look at The Resident Hotels. The one in Kensington is usually a little cheaper than the one in Victoria, Soho or Covent Garden. They have some rooms that sleep up to 4 people. They have a tiny little kitchenettes with mini-fridge, microwave, sink, utensils and coffee/tea makers.

https://www.residenthotels.com/

The Bailey's Hotel London Kensington would be a great choice. We stayed there in August with our daughter's family who have 2 children. They had a Luxury Room with 2 double beds which worked out well for them. It included breakfast and was 377 square feet. The Bailey's Hotel is in a great location across from the Gloucester Road tube station, so you can get anywhere in London easily. It also has restaurants and grocery stores nearby. Request a room with a street view which has wonderful daylight. Wishing you a great trip!

Take a look at Citadines - it’s an aparthotel type thing, with various bed configurations depending on family size, and kitchenettes as well.

Some good locations including Trafalgar Square and Holborn, both very central.

There are also hotels at the budget end that offer three or four bed rooms. Booking.com will help you find those.

Most standard hotel rooms in London just aren’t big enough for two double beds. It’s a cramped old city where square footage is very expensive.

Thank you everyone for your helpful suggestions! I'm researching them all.