Saturday in SW7 tends to follow the same script. Natural History Museum by ten, a squabble in the dinosaur shop by half eleven, two children who have gone off sandwiches. The walk from Exhibition Road down to Old Brompton Road takes about ten minutes, and it usually ends at Dozo — the family Japanese restaurant London parents in this postcode quietly pass on to each other.

Dozo has been on Old Brompton Road since 2011, with a second site on Old Compton Street in Soho since 2013. Both are contemporary Japanese kitchens — sushi, sashimi, maki — in cosy, modern rooms. Neither has cartoon menus or a ball pit. That is rather the point.

A family Japanese restaurant London families keep returning to

Japanese food in this city tends to be either very formal or very fast. Dozo sits in the useful middle. The rooms are contemporary rather than traditional — clean lines, warm lighting, dark wood — and the cooking suits a nine-year-old trying her first maki roll and an adult who wants proper sashimi at the same table.

South Kensington is the calmer of the two. It sits along Old Brompton Road, a short walk from the tube, and fills with a mixed crowd: local families, museum staff, students, office workers from the nearby buildings. At lunch you will spot buggies parked at the edge of tables and a relaxed crowd straight off the Science Museum. In the evening the room dims and quietens, which makes it easier to settle a tired child into a corner seat and eat at a civilised pace.

A family restaurant SW7 parents actually use has to do three things well: feed people quickly, handle a table of mixed ages, and never make anyone feel awkward about ordering the plainest thing on the menu. Dozo does all three. The kitchen keeps things simple, the servers are used to explaining what is what, and nobody minds a child who changes their mind halfway through and decides they would rather have rice than anything raw.

The menu is broad, which helps. Sushi and sashimi for the confident, maki rolls for the cautious, hot dishes for anyone who would rather not eat cold food at all. Beef nabe is the obvious one on a cold afternoon, and it is the sort of thing a teenager will happily share across the table. You can see the whole spread on the full South Kensington menu.

Evenings are gentler than you might expect. Music stays low, the pace slows, and if you are eating with children at seven o'clock you will not be the only table doing it. That is the thing about a good neighbourhood restaurant: it fits the evening you are actually having, not the one you had planned.

Both rooms have had time to settle into their neighbourhoods. The story behind Dozo covers how South Kensington came first and Soho followed.

Museum-day lunch in South Kensington

Natural History Museum, V&A, Science Museum, all in one day: brilliant, and a guaranteed meltdown by four o'clock. The trick is to sit down properly in the middle of it. Old Brompton Road is a few minutes from the station, which makes Dozo an easy stop on the way in or home.

Weekday lunch is the sweet spot. South Kensington lunch sets keep it simple: a defined spread rather than a long à la carte debate, which is exactly what you want when one child is starving and the other has lost interest in food entirely. The sets run through the week and the pace is quick. In and out inside an hour if you need to be, or stretched out with a pot of green tea while the table recovers.

For a family meal that feels like a treat rather than a refuelling stop, order a couple of things to share down the middle. A plate of maki, some nigiri, one hot bowl between you. Children are far more willing to try something when it sits on a shared plate and nobody makes a fuss about it.

One practical note: museum crowds arrive in waves, and between about twelve and half past one on a wet Saturday SW7 gets busy. No booking can mean a wait. Go early, go late, or ring ahead. Opening hours and directions are on the contact page.

The tube is straightforward too. South Kensington is on the Piccadilly, District and Circle lines, and the pedestrian tunnel from the station brings you out a couple of minutes from the restaurant — no road crossings with a buggy, no waiting for a bus in the rain. Coming from the other direction along Cromwell Road is just as easy.

Kid friendly sushi in South Kensington: a first-timer's route

If you are new to sushi, the menu can read like a wall of unfamiliar words. It isn't, really. Most of it comes down to three things: nigiri (a slice of fish over rice), sashimi (the fish on its own, no rice) and maki rolls (rice and filling rolled in seaweed, then sliced). Learn those three and everything else is a variation.

Start children on maki rolls. Small, tidy, easy to pick up with chopsticks or fingers, and not remotely intimidating to look at. Spider maki — a soft-shell crab roll — is a good next step for anyone feeling braver, because the texture is familiar even if the format isn't. From there, a piece of nigiri, then a sliver of sashimi for the ones who have decided they are experts.

That is what kid friendly sushi here really means: not a separate children's menu with chips on it, but a kitchen that lets a nine-year-old work up to raw fish in their own time. If someone at the table will not touch anything cold, the hot dishes and the beef nabe cover them nicely.

Two bits of advice. Order less than you think — sushi fills people up in a way that surprises them, and over-ordering leaves a lot of leftover rice and a bill nobody wanted. And let each child choose one thing, even if it is the safest item on the menu. A child who has picked their own roll tends to eat it.

Finish with green tea ice cream. Children either adore it or find it deeply suspicious, and both reactions are entertaining. Order one between two if you are unsure.

Counter seats, group tables and Friday nights in Soho

Soho is a different animal. The Old Compton Street site opened in 2013 and plays to the neighbourhood's strengths: theatreland on the doorstep, Chinatown a couple of minutes away, a crowd that eats late. On a Friday evening the room hums. Bring children early — half five or six, before the pre-theatre rush gets going — and you get the best of it.

There is counter seating here, and the counter doubles as a little sashimi corner where you can watch fish being sliced to order. A small piece of theatre, and children tend to be fascinated. For bigger groups — a birthday, grandparents visiting, two families sharing a table — ask for one of the larger tables when you book and order a few platters for the middle rather than everyone choosing separately. Not sure where to start? The sushi, sashimi and maki menu is the place to look, and there is a separate list for sake, Japanese whisky and cocktails.

Weekday lunch in Soho is a much quieter affair. The lunch sets run Monday to Friday, 12–3pm, and make a sensible choice if you are feeding a small group before a matinee. The Soho weekday lunch sets do the job quickly and without drama. Between the two sites, this is a family Japanese restaurant London families can use for anything from a rushed Wednesday lunch to a birthday dinner that runs long.

Questions families ask before they book

Is Dozo suitable for young children?

Yes. South Kensington is calm and easy in particular, and Soho works well if you go early. The teams are used to families and will happily explain dishes or point you towards something milder if a child is nervous about raw fish. Both rooms are cosy and modern rather than formal, so a bit of noise is not going to bother anyone.

Do we need to book?

Not always, but it is the safer bet at weekends, during school holidays and before theatre performances in Soho. Ring the restaurant directly — Soho on 020 7434 3219, South Kensington on 020 7225 0505 — or check the opening hours and directions before you set off.

What should a family order if nobody has eaten Japanese food before?

Shared plates, mostly. A couple of maki rolls to start, a plate of nigiri, one sashimi selection, and something hot or a beef nabe for the middle of the table. Add green tea ice cream at the end. If you want to see what it all looks like first, the photo gallery gives you a decent idea.

Ready to plan a lunch or an early dinner? Have a look at the South Kensington menu, or the Soho menu if you are heading into town, then check directions and opening hours before you come. Walk-ins are welcome, but a quick call ahead makes a family table much easier to sort.