Where to stay in London - family of 4

Need more info.
Budget? Priorities for a room apartment/hotel? What are your interests while there?

Two bedroom flat minutes to Westminster, London Eye. One queen bed in one bedroom, twin beds in the other.
Good location, reasonable price. Furnishings look a bit worn, but owner is quite responsive.
https://www.vrbo.com/439545ha?adultsCount=4&arrival=2022-07-11&departure=2022-07-16&unitId=1065757

Thank you for your replies! We are traveling on a budget but only going once so don't want to be too cheap!! We plan on only staying in London a couple of days before we head to Paris. We are just going to hit the highlights as 3 of the 4 of us have been there before. We are open to hotel, apartment, etc. but with 2 adult children ( 1 a male and 1 a female) Thank you for any helpful advice.

Look at the Premier Inns, check Vrbo. Stay in Zone 1.

Most Premier Inn rooms seem to have one largish bed (size varies) and one comfortable day-bed that can be made up into a single (twin-sized) bed. I believe some of the hotels do have rooms with two larger beds, but you're probably going to want three beds, which may be trickier. The Premier Inn website doesn't even allow you to indicate there will be more than two adults in a room. (I don't know why; the hotels are well-managed but the website can be frustrating.)

While waiting for additional uggestions from experienced posters here, it may be worthwhile to try booking.com. You can set appropriate filters for your needs, including your price range per night. Don't forget to specify air conditioning if necessary. The website will give you options for housing four adults in all sorts of configurations--probably a few quad rooms, maybe a triple room and a single, and lots of hotels that might have two double rooms available. Booking.com also lists some apartments. This will at least give you an idea of what sorts of configurations are available in your price range for your travel period.

Premier Inns are fine, but pretty corporate and very low on the "quaint scale" if that means anything to you.

My go-to place is the Celtic Hotel, near Russell Square Tube Station in Bloomsbury. Easily walkable to British Museum, Soho/West End, Regents Park, and Holborn/Chancery Lane/St Paul's. Great English breakfast included, and a nice pub round the corner (the Friend at Hand).

hey hey ptgilbert
what are your dates in london? are you taking the eurostar to paris and what is that date and are you flying out of paris? do you have a place to stay in paris?
many people are traveling now and especially summer time, not wanting to be cooped up anymore. places are booking up fast and you have 4 of you which can be tough to get since places a very small. filter out you wants and needs, budget, how many beds, A/C if it's the summer.
buy your eurostar tickets early for a cheaper fare. read all the fine print and rules about riding the eurostar. few years ago us 3 friends got a discount for 3 of us, but things may have changed now. good luck
remember that check-in to hotels/apts are not until 2-4pm unless you can get an early check-in or rent the night before and explain why. that way you can get room in morning of arrival, sounds crazy but have seen it and been there just waiting for hours and what to do with luggage. learned real fast and schedule for early afternoon on whatever transportation you take.
aloha

The Victoria neighborhood is where you’ll find cheaper accommodation.